Let A be an n n matrix, then the following properties can be mentioned for determinants, where det [ A] = A .

Let s consider the following relationship:

Inner product or dot product is given as

Outer product is given as

The inner and outer products are related as follows:

Given a square matrix, A, we can write down the following relationships with ? = eigenvalue and v = eigenvector.

For Hermitian matrices, we provide the mathematical relationship between the arithmetic mean and the geometric mean.

A square Hermitian matrix can be diagonalized as

where D diagonal matrix, { ? ₀, ? ₁, ___, ? _{M ?1}}, and U is a unitary matrix, U* U = I or U* = U ^?1.

We can define a Rayleigh quotient as

The Frobenius or Euclidean norm is given as