A square matrix with real numbers or values is termed as an orthogonal matrix if its transpose is equal to the inverse matrix of it. In other words, the product of a square orthogonal matrix and its transpose will always give an identity matrix.

How do you know if a matrix is orthogonal?

How to Know if a Matrix is Orthogonal? To check if a given matrix is orthogonal, first find the transpose of that matrix. Then, multiply the given matrix with the transpose. Now, if the product is an identity matrix, the given matrix is orthogonal, otherwise, not.

What does it mean when a matrix is orthogonal?

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... The determinant of any orthogonal matrix is either +1 or −1.