## diagonal matrix

### a square nxn matrix whose non diagonal entries are zero

A diagonal matrix is a special type of matrix where all the off-diagonal elements are zero and only the diagonal elements have non-zero values. In other words, it is a square matrix in which non-diagonal elements are equal to zero, while the diagonal elements can be any value, including zero.

For example, consider the matrix:

\begin{bmatrix}

5 & 0 & 0 \\

0 & 8 & 0 \\

0 & 0 & 2 \\

\end{bmatrix}

This is a diagonal matrix because all the non-diagonal elements are zero. The diagonal elements are 5, 8, and 2.

Diagonal matrices have important applications in linear algebra, particularly in the diagonalization of matrices. They are also useful in solving linear systems of equations and in computing the determinant of a matrix.

One interesting property of diagonal matrices is that they are their own eigenvalue matrices. That is, the eigenvalues of a diagonal matrix are simply its diagonal elements. This makes calculating eigenvalues and eigenvectors of diagonal matrices very simple.

Overall, diagonal matrices are a simple yet important concept in linear algebra that have a wide range of applications.

##### More Answers:

Mastering the Methods of Solving Linear Equations: Your Guide to Graphical, Elimination, Substitution, and Matrix MethodsExplore The Importance And Applications Of Unit Matrix In Linear Algebra: Its Properties And Notation (I_N)

Zero Matrices In Linear Algebra: Properties, Applications, And Examples