Similar Matrices

What is matrix?

A “matrix” is referred to as a rectangular array of numbers that are arranged in rows and columns. The horizontal lines are said to be rows, while the vertical lines are said to be columns.

Define similar matrices.

Two square matrices A and B of the same order are said to be similar, if and only if there exists an invertible matrix “P” of the same order as A and B such that:

P^-1AP = B

Are the determinants of two similar matrices the same?

Yes, two similar matrices A and B are said to have the same determinants, i.e., det (A) = det (B).

A “matrix” is referred to as a rectangular array of numbers that are arranged in rows and columns. The horizontal lines are said to be rows, while the vertical lines are said to be columns. We can determine the size of a matrix by the number of rows and columns in it. If a matrix has “m” rows and “n” columns, then it is said to be an “m by n” matrix and is written as an “m × n” matrix.

For example, a matrix with five rows and three columns is a “5 × 3” matrix. We have various types of matrices, like rectangular, square, triangular, symmetric, singular, etc. In this article, we learn about similar matrices, their examples, and their properties.