The first fundamental form may be represented as a symmetric matrix.

In case of a symmetric matrix S as before, one has .

In particular if is a real symmetric matrix, they are the same except for transposition.

Also if then while and again the reader may check that the product of the symmetric matrices.

Assume for the moment that is a symmetric matrix.

Thus is expressible as the product of two symmetric matrices.

Quadratic forms can be expressed as where is a symmetric matrix.

In the case of the real symmetric matrix, we see that , so clearly holds.

The symmetric matrix of diffusion coefficients should be positive definite.

However, if products of three symmetric matrices are considered, any permutation is allowed.

He also showed, in 1829, that the eigenvalues of symmetric matrices are real.

It is a symmetric matrix consisting of nine 3x3 circulant blocks.

Denote by the space of all real symmetric matrices.

If the function's image and domain both have a potential, then these fit together into a symmetric matrix known as the Hessian.

The matrix A in the above decomposition is a symmetric matrix.

A real and symmetric matrix is simply a special case of a Hermitian matrix.

Let A be a symmetric matrix of reals.

The reciprocal R of a symmetric matrix is itself symmetric.

Let be a p x p symmetric matrix of random variables that is positive definite.

Moreover, a symmetric matrix "A" is uniquely determined by the corresponding quadratic form.

Non-uniform scaling is accomplished by multiplication with any symmetric matrix.

Otherwise, a skew-symmetric matrix is just the same thing as a symmetric matrix.

"Numerical computation of the characteristic values of a real symmetric matrix".

A symmetric matrix is positive-definite if and only if all its eigenvalues are positive.

Here is a real symmetric matrix.