{"id":4861,"date":"2021-08-31T17:47:40","date_gmt":"2021-08-31T17:47:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=4861"},"modified":"2022-01-16T17:01:09","modified_gmt":"2022-01-16T11:31:09","slug":"different-types-of-matrices","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/different-types-of-matrices\/","title":{"rendered":"Different Types of Matrices – Definitions and Examples"},"content":{"rendered":"

Here you will what is matrix and definitions of different types of matrices with examples.<\/p>\n

Let’s begin –<\/p>\n

What is Matrix ?<\/h2>\n

A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m \\(\\times\\) n matrix (to be read as m by n matrix).<\/p>\n

A m by n matrix is usually written as<\/p>\n

A = \\(\\begin{bmatrix}a_{11} & a_{12} & …… & a_{1n} \\\\ a_{21} & a_{22} & …… & a_{2n}\\\\  . & . & . \\\\ a_{m1} & a_{m2} & …… & a_{mn}  \\end{bmatrix}\\)<\/p>\n

Different Types of Matrices<\/h2>\n

All different types of matrices with examples are given below :<\/p>\n

Row Matrix<\/strong><\/h4>\n

A matrix having only one row is called a row matrix or a row-vector.<\/p>\n

Example : A = [ 1 2 -1 2 ] is a row matrix of order \\(1 \\times 4\\).<\/p>\n

Column Matrix<\/strong><\/h4>\n

A matrix having only one column is called a column matrix or a column vector.<\/p>\n

Example : \\(\\begin{bmatrix} 1 \\\\ 2 \\\\ -1  \\end{bmatrix}\\) is a column matrix of order \\(3 \\times 1\\).<\/p>\n

Square Matrix<\/strong><\/h4>\n

A matrix in which number of rows is equal to the number of columns, say n, is called a square matrix of order n.<\/p>\n

Example : the matrix \\(\\begin{bmatrix} 2 & 1 & -1 \\\\ 3 &  -2 & 5 \\\\ 1 & 5 &  -3  \\end{bmatrix}\\) is a square matrix of order \\(3 \\times 3\\) in which diagonal elements are 2, -2 and -3.<\/p>\n

Diagonal Matrix<\/strong><\/h4>\n

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.<\/p>\n

Example : the matrix \\(\\begin{bmatrix} 1 & 0 & 0 \\\\ 0 &  2 & 0 \\\\ 0 & 0 &  3  \\end{bmatrix}\\) is a diagonal denoted by A = diag [1, 2, 3].<\/p>\n

Scalar Matrix<\/strong><\/h4>\n

A square matrix A = \\([a_{ij}]_{n\\times n}\\) is called a scalar matrix if<\/p>\n

(i) \\(a_{ij}\\) = 0 for all i \\(\\ne\\) j and,<\/p>\n

(ii) \\(a_{ii}\\) = c, for all i, where c \\(\\ne\\) 0<\/p>\n

In other words, a diagonal matrix in which all the diagonal elements are equal is called the scalar matrix.<\/p>\n

Example : the matrix \\(\\begin{bmatrix} 2 & 0  \\\\ 0 &  2  \\end{bmatrix}\\) is scalar martix of order 2.<\/p>\n

Identity or Unit Matrix<\/strong><\/h4>\n

A square matrix A = \\([a_{ij}]_{n\\times n}\\) is called a identity or unit matrix if<\/p>\n

(i) \\(a_{ij}\\) = 0 for all i \\(\\ne\\) j and,<\/p>\n

(ii) \\(a_{ii}\\) = 1, for all i<\/p>\n

In other words, a diagonal matrix in which all the diagonal elements is unity is called the unit matrix.<\/p>\n

The identity matrix of order n is denoted by \\(I_n\\).<\/p>\n

Example : the matrix \\(I_2\\) = \\(\\begin{bmatrix} 1 & 0  \\\\ 0 &  1  \\end{bmatrix}\\) is identity matrix of order 2.<\/p>\n

Null Matrix<\/strong><\/h4>\n

A matrix in which al elements are zero is called  a null or a zero matrix,<\/p>\n

Example : the matrix \\(\\begin{bmatrix} 0 & 0  \\\\ 0 &  0  \\end{bmatrix}\\) is null matrix of order 2.<\/p>\n

Upper Triangular Matrix<\/strong><\/h4>\n

A square matrix A = \\([a_{ij}]\\) is called an upper triangular matrix if \\(a_{ij}\\) = 0 for all  i > j.<\/p>\n

Thus, in an upper triangular matrix, all elements below the main diagonal are zero.<\/p>\n

Example : \\(\\begin{bmatrix} 1 & 3 & 4 \\\\ 0 &  4 & 5 \\\\ 0 & 0 &  7  \\end{bmatrix}\\) is a upper triangular matrix.<\/p>\n

Lower Triangular Matrix<\/strong><\/h4>\n

A square matrix A = \\([a_{ij}]\\) is called an lower triangular matrix if \\(a_{ij}\\) = 0 for all  i < j.<\/p>\n

Thus, in an lower triangular matrix, all elements above the main diagonal are zero.<\/p>\n

Example : \\(\\begin{bmatrix} 1 & 0 & 0 \\\\ 2 &  3 & 0 \\\\ 1 & 6 &  5  \\end{bmatrix}\\) is a lower triangular matrix.<\/p>\n\n\n

\n
Next – Equality of Matrices<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will what is matrix and definitions of different types of matrices with examples. Let’s begin – What is Matrix ? A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m \\(\\times\\) n matrix (to be read as …<\/p>\n

Different Types of Matrices – Definitions and Examples<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[34],"tags":[489,488,490],"yoast_head":"\nDifferent Types of Matrices - Definitions and Examples<\/title>\n<meta name=\"description\" content=\"In this post you will what is matrix and definitions of different types of matrices 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\/different-types-of-matrices\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Different Types of Matrices - 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