What is Diagonal matrix?

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is {\displaystyle \left} , while an example of a 3×3 diagonal matrix is {\displaystyle \left} . An identity matrix of any size, or any multiple of it , is a diagonal matrix.

A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale. Its determinant is the product of its diagonal values.