# Diagonal matrix

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In linear algebra, a **diagonal matrix** is a particular type of square matrix. The main-diagonal may contain any real values, but the elements that do not coincide with the main-diagonal must all be zeros.

In particular, given any ring with additive identity given by , a matrix (an -by- matrix whose entries are elements of ) is said to be a diagonal matrix if for any and such that , , where denotes the -th entry.

An identity matrix is a special case of the diagonal matrix.

A matrix is considered diagonalizable if it is similar to a diagonal matrix. The process of finding the similar diagonal matrix is called diagonalization.

Diagonal matrices are very useful computationally, since