**17.3****
****Symmetric Matrices** (.NET, C#, CSharp, VB, Visual Basic, F#)

A *symmetric* matrix is a
square matrix that satisfies where denotes
the transpose of . That
is, for all . For example, this is a
4 x 4 symmetric matrix:

Symmetric matrices are often used to represent quadratic forms.

**NMath**
provides symmetric matrix classes for single- and double-precision floating
point numbers. The classnames are **FloatSymmetricMatrix**
and **DoubleSymmetricMatrix**.
Hermitian matrices are a generalization of symmetric matrices for complex
types (Section 17.4).

For efficiency, only the upper triangle is stored. The storage scheme is the same as for an upper triangular matrix (Section 17.2).