Here you will learn what is row matrix definition and order of row matrix with examples. Let’s begin – Row Matrix Definition : A matrix having only one row is called a row-matrix or a row-vector. It is matrix having all its elements in a single row. It has one row and multiple columns. The …
Here you will learn what is involutory matrix with examples. Let’s begin – Involutory Matrix If \(A^2\) = I . the matrix A is said to be an involutory matrix, i.e. the square roots of the identity matrix (I) is involutory matrix. Note : The determinant value of this matrix (A) is 1 or -1. …
Here you will learn what is nilpotent matrix with examples. Let’s begin – Nilpotent Matrix A square matrix of the order ‘n’ is said to be a nilpotent matrix of order m, m \(\in\) N if \(A^m\) = O & \(A^{m-1}\) \(\ne\) O. Example : Show that A = \(\begin{bmatrix} 1 & 1 & 3 …
Here you will learn what is periodic matrix with examples. Let’s begin – Periodic Matrix A square matrix which satisfies the relation \(A^{k+1}\) = A for some positive integer k, is called a periodic matrix. The period of the matrix is the least value of k for which \(A^{k+1}\) = A holds true. Note that …
Here you will learn what is idempotent matrix with examples. Let’s begin – Idempotent Matrix A square matrix is idempotent matrix provided \(A^2\) = A. For this matrix note the following : (i) \(A^n\) = A \(\forall\) n \(\ge\) 2, n \(\in\) N. (ii) The determinant value of this matrix is either 1 or 0. …
Here you will learn formula for inverse of a matrix and properties of inverse of matrix with example. Let’s begin – Formula for Inverse of a Matrix A square matrix A said to be invertible if and only if it is non-singular (i.e. |A| \(\ne\) 0) and there exists a matrix B such that, AB …
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Here you will learn how to find adjoint of the matrix 2×2 and 3×3, cofactors and its properties with examples. Let’s begin – Adjoint of the Matrix Let A = \([a_{ij}]\) be a square matrix of order n and let \(C_{ij}\) be a cofactor of \(a_{ij}\) in A. Then the transpose of the matrix of …
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Here you will learn how to find trace of matrix, its properties and what is orthogonal matrix with example. Let’s begin – Trace of Matrix The sum of the elements of the square matrix A lying along the principal diagonal is called the trace of A i.e (tr(A)). Thus if A = \([a_{ij}]_{n\times n}\), then …
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Here you will learn what are symmetric and skew symmetric matrices with examples. Let’s begin – Symmetric and Skew Symmetric Matrices Symmetric Matrix A square matrix A = \([a_{ij}]\) is called a symmetric matrix, if \(A^T\) = A or \(a_{ij}\) = \(a_{ji}\) for all i, j. for example, the matrix A = \(\begin{bmatrix} 3 & …
Here you will learn what is transpose of matrix with definition and examples. Let’s begin – What is Transpose of Matrix Let A = \([a_{ij}]\) be a \(m\times n\) matrix. Then the transpose of A, denoted by \(A^{T}\) or A’, is an \(n\times m\) matrix such that \((A^T)_{ij}\) = \(a_{ji}\) for all i = 1, …
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