When the conjugate transpose of a complex square matrix is equal to itself, then such matrix is known as hermitian matrix. If B is a complex square matrix and if it satisfies Bθ = B then such matrix is termed as hermitian. Here Bθ represents the conjugate transpose of matrix B. The conjugate transpose of a matrix … Read more
Orthogonal matrix is a square matrix R=[xij] such that RT = R-1. In other words, a square matrix (R) whose transpose is equal to its inverse is known as orthogonal matrix i.e. RT = R-1. Orthogonal matrix examples The best example of an orthogonal matrix is an identity matrix or unit matrix as shown below. \[I=\begin{bmatrix} 1 &0 … Read more
Skew symmetric matrix is a square matrix Q=[xij] in which (i, j)th element is negative of the (j, i)th element i.e. xij = -xji for all values of i and j. In other words, a square matrix (Q) which is equal to negative of its transpose is known as skew-symmetric matrix i.e. QT = -Q. Skew symmetric matrix examples The example … Read more
Symmetric matrix is a square matrix P=[xij] in which (i, j)th element is similar to the (j, i)th element i.e. xij = xji for all values of i and j. In other words, a square matrix (P) which is equal to its transpose is known as symmetric matrix i.e. PT = P. Symmetric matrix examples The … Read more
Singular matrix is a square matrix whose determinant is zero. It is also known as non invertible matrix or degenerate matrix. A square matrix whose determinant is not zero is known as non singular matrix. It is also known as invertible matrix or non degenerate matrix. A square matrix P is said to be singular matrix … Read more
Lower triangular matrix is a square matrix whose upper off-diagonal elements are zero. It is usually denoted by the capital letter ‘L‘. A square matrix Q = [xij] is said to be lower triangular matrix (LTM) if xij = 0 when i < j. Note: In this matrix, the diagonal and/or lower off-diagonal elements may or may not … Read more
Upper triangular matrix is a square matrix whose lower off-diagonal elements are zero. It is usually denoted by the capital letter ‘U‘. A square matrix P = [xij] is said to be upper triangular matrix (UTM) if xij = 0 when i > j. Note: In such matrix, the diagonal and/or upper off-diagonal elements may or may not be zero. … Read more
Zero Matrix is a type of matrix whose elements are equal to zero. Zero matrix is also known as null matrix. It is generally denoted by capital letter ‘O‘. A matrix O = [xij] is said to be null matrix or zero matrix if xij = 0 for all values of ‘i‘ and ‘j‘. This … Read more
Unit Matrix or Identity Matrix is a square matrix whose all diagonal elements is 1 and all off-diagonal elements are zero. It is usually denoted by the capital letter ‘I‘. A square matrix P = [xij] is said to be unit matrix or identity matrix if xij = 1 when i = j and xij = … Read more
A square matrix is a type of matrix in which number of rows is equal to number of columns. Matrix P = [xij]m x n is said to be a square matrix when m = n. Here m is the number of rows and n is the number of columns. A square matrix P of … Read more