{"id":308,"date":"2023-07-06T12:44:55","date_gmt":"2023-07-06T12:44:55","guid":{"rendered":"https:\/\/mathority.org\/id\/matriks-diagonal\/"},"modified":"2023-07-06T12:44:55","modified_gmt":"2023-07-06T12:44:55","slug":"matriks-diagonal","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/matriks-diagonal\/","title":{"rendered":"Matriks diagonal"},"content":{"rendered":"<p>Pada halaman ini Anda akan melihat apa itu matriks diagonal dan contoh matriks diagonal. Selain itu, Anda akan mempelajari cara mengoperasikan matriks jenis ini, cara menghitung determinannya dengan mudah, dan cara membalikkannya. Ada juga sifat dan penerapan matriks diagonal. Dan terakhir, penjelasan tentang matriks bidiagonal dan matriks tridiagonal.<\/p>\n<h2 class=\"wp-block-heading\"> Apa itu matriks diagonal?<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks diagonal<\/strong> adalah matriks persegi yang semua elemen di luar diagonal utamanya bernilai nol (0). Elemen diagonal utama mungkin nol atau tidak.<\/p>\n<p> Setelah kita mengetahui definisi pasti dari matriks diagonal, kita akan melihat contoh matriks diagonal:<\/p>\n<h2 class=\"wp-block-heading\"> Contoh matriks diagonal<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Contoh matriks diagonal berdimensi 2\u00d72<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-matrice-diagonale-22152-1.webp\" alt=\"Contoh Matriks Diagonal 2x2\" class=\"wp-image-1728\" width=\"73\" height=\"74\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Contoh matriks diagonal berorde 3\u00d73<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-matrice-diagonale-32153-1.webp\" alt=\"Contoh matriks diagonal 3x3\" class=\"wp-image-1729\" width=\"125\" height=\"114\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">Contoh matriks diagonal berukuran 4\u00d74<\/span> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-matrice-diagonale-42154-1.webp\" alt=\"Contoh Matriks Diagonal 4x4\" class=\"wp-image-1730\" width=\"161\" height=\"143\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Matriks jenis ini umumnya ditulis dengan menunjukkan unsur-unsur diagonalnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14216c3a6fd6e7bfd4c9d78ac2a4765c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"diag(2,5,1) = \\left. \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"196\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Operasi dengan matriks diagonal<\/h2>\n<p> Salah satu alasan matriks diagonal sangat penting dalam aljabar linier adalah karena matriks tersebut memudahkan Anda dalam melakukan perhitungan. Inilah sebabnya mengapa mereka begitu digunakan dalam matematika.<\/p>\n<h3 class=\"wp-block-heading\"> Penjumlahan dan pengurangan matriks diagonal<\/h3>\n<p> Menjumlahkan (dan mengurangkan) dua matriks diagonal sangatlah sederhana: cukup tambahkan (atau kurangi) angka-angka pada diagonalnya.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6f7d2e19d548ee0d53465992ebac7fb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{diag}(a_1,... ,a_n) \\pm \\text{diag}(b_1 ,... , b_n) = \\text{diag}(a_1\\pm b_1,..., a_n\\pm b_n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"454\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Misalnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e659649fca7fe55f33c0f3452e8c46f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; -2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} +\\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; -4 \\end{pmatrix} = \\begin{pmatrix} 6&amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"333\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Perkalian matriks diagonal<\/h3>\n<p> Untuk menyelesaikan perkalian atau hasil kali matriks dua matriks diagonal, cukup mengalikan elemen-elemen diagonalnya.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88d1625220fe5fd9bda3767f15b59372_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{diag}(a_1,... ,a_n) \\cdot \\text{diag}(b_1 ,... , b_n) = \\text{diag}(a_1\\cdot b_1,..., a_n\\cdot b_n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"427\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Misalnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0bcb4a59778cc41eed67dce0bc384682_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; -4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; -3 \\end{pmatrix} \\cdot\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; -2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} = \\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; -18 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"361\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"> Kekuatan matriks diagonal<\/h3>\n<p> Untuk menghitung pangkat matriks diagonal, kita perlu menaikkan setiap elemen diagonal menjadi eksponen:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fcfe6475c0d4ea75691ed4c9bdaa64cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\text{diag}(a_1,... ,a_n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b93b6a0717632e9bee22dcc5f5799f63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A^k= \\text{diag}(a_1^k,... ,a_n^k)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"157\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Misalnya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4d27337283f4b6029bff166fb8e3458d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left. \\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix}\\right.^3= \\begin{pmatrix} 27 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 64 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"89\" width=\"221\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> Penentu matriks diagonal<\/h2>\n<p> <strong>Penentu matriks diagonal<\/strong> adalah hasil kali elemen-elemen pada diagonal utama.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fcfe6475c0d4ea75691ed4c9bdaa64cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\text{diag}(a_1,... ,a_n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-326faa61bf2e51b299c2b0274c7c0416_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}(A)= \\prod_{i =1}^n a_i\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"115\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p> Lihatlah latihan penyelesaian berikut ini di mana kita mencari determinan matriks diagonal hanya dengan mengalikan elemen-elemen diagonal utamanya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f34514c6e1559b8ebb296ee6c51a33d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{vmatrix} = 5 \\cdot 2 \\cdot 3 = 30\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Teorema ini mudah dibuktikan: Anda hanya perlu menghitung determinan matriks diagonal dengan blok (atau kofaktor). <strong>Demonstrasi<\/strong> ini dirinci di bawah ini menggunakan matriks diagonal umum:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b8718172b4b70d1ccacb01ea7ed5dd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\begin{vmatrix} a &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; b &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; c \\end{vmatrix}&amp;  = a \\cdot \\begin{vmatrix} b &amp; 0 \\\\[1.1ex] 0 &amp; c \\end{vmatrix} - 0 \\cdot \\begin{vmatrix} 0 &amp; 0 \\\\[1.1ex] 0 &amp; c \\end{vmatrix} + 0 \\cdot \\begin{vmatrix} 0 &amp; b \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (b\\cdot c) - 0 \\cdot 0 + 0 \\cdot 0 \\\\[2ex] &amp; = a \\cdot b \\cdot c \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"166\" width=\"337\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"> Membalikkan matriks diagonal<\/h2>\n<p> Suatu matriks diagonal <strong>dapat dibalik jika dan hanya jika semua elemen diagonal utama berbeda dari 0<\/strong> . Dalam hal ini kita katakan bahwa matriks diagonalnya adalah matriks beraturan.<\/p>\n<p> Selain itu, invers suatu matriks diagonal akan selalu berupa matriks diagonal lain dengan <strong>invers<\/strong> diagonal utama:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a91beaaca82477a0c882b42da4eb7481_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A= \\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 8 \\end{pmatrix}  \\ \\longrightarrow \\ A^{-1}=\\begin{pmatrix} \\frac{1}{3} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; \\frac{1}{2} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; \\frac{1}{8} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"324\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dari uraian sebelumnya, kita dapat menyimpulkan bahwa determinan invers suatu matriks diagonal adalah hasil kali invers diagonal utama: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0571390802f955fac935aeb9cf4ab92f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle B= \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; -1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae2b6aa1dd4d6405d30753e66e7f7486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\left| B^{-1}\\right|=\\cfrac{1}{2} \\cdot \\cfrac{1}{4} \\cdot \\cfrac{1}{-1}=-\\cfrac{1}{8} = -0,125\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"266\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> Sifat-sifat matriks diagonal<\/h2>\n<ul>\n<li> Setiap matriks diagonal juga merupakan <a href=\"https:\/\/mathority.org\/id\/contoh-matriks-simetris-dan-sifat-sifatnya\/\">matriks simetris<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> Matriks diagonal adalah <a href=\"https:\/\/mathority.org\/id\/matriks-segitiga-atas-bawah\/\">matriks yang berbentuk segitiga atas dan segitiga bawah<\/a> .<\/li>\n<\/ul>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Matriks identitasnya<\/strong><\/span> adalah matriks diagonal:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4e4e9931fb7ae104414006cee93978a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Demikian pula <span style=\"color:#1976d2;\"><strong>matriks nol<\/strong><\/span> juga merupakan matriks diagonal, karena semua elemennya yang tidak berada pada diagonalnya adalah nol. Meskipun angka pada diagonalnya adalah 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-edb061dcbc869eba51ece12af43f796f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 0 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Nilai eigen (atau nilai eigen)<\/strong><\/span> suatu matriks diagonal adalah elemen-elemen diagonal utamanya.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1dea3de2ae28d46194ead012bc001cf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix} \\longrightarrow \\ \\lambda = 3 \\ ; \\ \\lambda = 4 \\ ; \\ \\lambda = 7\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"298\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> Suatu matriks persegi adalah diagonal jika dan hanya jika matriks tersebut <span style=\"color:#1976d2;\"><strong>berbentuk segitiga dan normal<\/strong><\/span> .<\/li>\n<\/ul>\n<ul>\n<li> <span style=\"color:#1976d2;\"><strong>Adjoint<\/strong><\/span> suatu matriks diagonal adalah matriks diagonal lainnya. <\/li>\n<\/ul>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> Aplikasi Matriks Diagonal<\/h2>\n<p> Seperti yang telah kita lihat, menyelesaikan perhitungan dengan matriks diagonal sangat sederhana, karena banyak angka nol yang terlibat dalam operasinya. Oleh karena itu, mereka sangat berguna dalam bidang matematika dan digunakan secara luas.<\/p>\n<p> Oleh karena itu, banyak penelitian telah dilakukan tentang cara <strong>mendiagonalisasi suatu matriks<\/strong> dan bahkan telah dikembangkan metode untuk mendiagonalisasi matriks (menggunakan polinomial karakteristik).<\/p>\n<p> Oleh karena itu, matriks yang dapat didiagonalisasi juga cukup relevan. Seperti teorema dekomposisi spektral, yang menetapkan kondisi kapan suatu matriks dapat didiagonalisasi dan kapan tidak.<\/p>\n<h2 class=\"wp-block-heading\"> matriks bidiagonal<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks bidiagonal<\/strong> adalah matriks persegi yang semua elemennya yang tidak berada pada diagonal utama atau diagonal atas atau bawah bernilai 0.<\/p>\n<p> Misalnya: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-25\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9acdfc09d0167548ef3f6f5b58d9276_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 3 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; -5 &amp; 1 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"94\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <strong>matriks bidiagonal atas<\/strong> <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b2b53f238add73431696006f4b05a2d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 6 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"80\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <strong>matriks bidiagonal yang lebih rendah<\/strong><\/p>\n<\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Ketika diagonal utama dan superdiagonal pertama terisi, kita berbicara tentang matriks bidiagonal atas. Di sisi lain, ketika diagonal utama dan subdiagonal pertama terisi, kita berbicara tentang matriks bidiagonal yang lebih rendah.<\/p>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h2 class=\"wp-block-heading\"> matriks tridiagonal<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>Matriks tridiagonal<\/strong> adalah matriks persegi yang elemen-elemen bukan nolnya hanyalah diagonal utama dan diagonal-diagonal yang berdekatan di atas dan di bawahnya.<\/p>\n<p> Misalnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9a8fbe0404c447268a89ff954e3b23d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 2 &amp; 3 &amp; 0 &amp; 0  \\\\[1.1ex] -4 &amp; 5 &amp; 9 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 6 &amp; -2 \\\\[1.1ex] 0 &amp; 0 &amp; 8 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"133\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jadi, semua matriks diagonal, bidiagonal, dan tridiagonal merupakan contoh <strong>matriks pita<\/strong> . Karena matriks pita adalah matriks yang semua elemen bukan nolnya mengelilingi diagonal utama.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pada halaman ini Anda akan melihat apa itu matriks diagonal dan contoh matriks diagonal. Selain itu, Anda akan mempelajari cara mengoperasikan matriks jenis ini, cara menghitung determinannya dengan mudah, dan cara membalikkannya. Ada juga sifat dan penerapan matriks diagonal. Dan terakhir, penjelasan tentang matriks bidiagonal dan matriks tridiagonal. Apa itu matriks diagonal? Matriks diagonal adalah &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/matriks-diagonal\/\"> <span class=\"screen-reader-text\">Matriks diagonal<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[64],"tags":[],"class_list":["post-308","post","type-post","status-publish","format-standard","hentry","category-jenis-tabel"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Matriks diagonal - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/matriks-diagonal\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Matriks diagonal - Mathority\" \/>\n<meta property=\"og:description\" content=\"Pada halaman ini Anda akan melihat apa itu matriks diagonal dan contoh matriks diagonal. 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