What is Orthogonal Matrix? Determinant and Examples

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

What is Skew Symmetric Matrix? Properties and Examples

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

Singular Matrix & Non Singular Matrix – Properties and Examples

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

What is Upper Triangular Matrix? Determinant and Examples

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