{"id":9993,"date":"2022-02-08T23:38:29","date_gmt":"2022-02-08T18:08:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=9993"},"modified":"2022-02-08T23:38:31","modified_gmt":"2022-02-08T18:08:31","slug":"diagonal-matrix-definition-and-examples","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/diagonal-matrix-definition-and-examples\/","title":{"rendered":"Diagonal Matrix – Definition and Examples"},"content":{"rendered":"

Here you will learn what is the diagonal matrix definition and order of diagonal matrix with examples.<\/p>\n

Let’s begin –<\/p>\n

Diagonal Matrix<\/h2>\n

Definition<\/strong> : A square matrix<\/a> A = \\([a_{ij}]_{n\\times n}\\) is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero<\/p>\n

i.e. \\(a_{ij}\\) = 0\u00a0 for all i \\(\\ne\\) j.<\/p><\/blockquote>\n

A diagonal matrix of order \\(n \\times n\\) having \\(d_1\\), \\(d_2\\), …. , \\(d_n\\) as diagonal elements is denoted by \\(diag[d_1, d_2, …. , d_n]\\).<\/p>\n

Also Read<\/strong> : Different Types of Matrices \u2013 Definitions and Examples<\/a><\/p>\n

Examples :<\/h2>\n

1).<\/strong> \\(\\begin{bmatrix} 1 & 0 & 0 \\\\ 0 &\u00a0 2 & 0 \\\\ 0 & 0 &\u00a0 3\u00a0 \\end{bmatrix}\\) is a diagonal matrix.<\/p>\n

The order of above matrix is \\(3 \\times 3\\) and it is denoted by diag[1, 2, 3].<\/p>\n

2).<\/strong> \\(\\begin{bmatrix} 2 & 0 \\\\ 0 &\u00a0 -2 \\end{bmatrix}\\) is a diagonal matrix.<\/p>\n

The order of above matrix is \\(2 \\times 2\\) and it is denoted by diag[2, -2].<\/p>\n

3).<\/strong> \\(\\begin{bmatrix} 1 & 0 & 0 & 0 \\\\ 0 &\u00a0 2 & 0 & 0 \\\\ 0 & 0 &\u00a0 3 & 0 \\\\ 0 & 0 & 0 & 4\u00a0 \\end{bmatrix}\\) is a diagonal matrix.<\/p>\n

The order of above matrix is \\(4 \\times 4\\) and it is denoted by diag[1, 2, 3, 4].<\/p>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the diagonal matrix definition and order of diagonal matrix with examples. Let’s begin – Diagonal Matrix Definition : A square matrix A = \\([a_{ij}]_{n\\times n}\\) is called a diagonal matrix if all the elements, except those in the leading diagonal, are zero i.e. \\(a_{ij}\\) = 0\u00a0 for all i …<\/p>\n

Diagonal Matrix – Definition and Examples<\/span> Read More »<\/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":"default","ast-global-header-display":"","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":""},"categories":[34],"tags":[872,873],"yoast_head":"\nDiagonal Matrix - Definition and Examples - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the diagonal matrix definition and order of diagonal matrix with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/diagonal-matrix-definition-and-examples\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Diagonal Matrix - 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