# Symmetric matrix

In

linear algebra, a

**symmetric matrix** is a

matrix that is its own

transpose. Thus

*A* is symmetric if:

which implies that

*A* is a

square matrix.
Intuitively, the entries of a symmetric matrix are symmetric with respect to the

main diagonal (top left to bottom right). Example:

Any

diagonal matrix is symmetric, since all its off-diagonal entries are zero.

One of the basic theorems concerning such matrices is the finite-dimensional spectral theorem, which says that any symmetric matrix whose entries are real can be diagonalized by an orthogonal matrix.

See also skew-symmetric matrix.