**Definition of a matrix:**

Any 2-dimensional array of real or complex numbers.

**Square matrix:**

A matrix of type .

**Diagonal**:

The entries of a square matrix in the i-th line and i-th column (same index i), for some i.

**Identity matrix:**

A square matrix with 1’s on the diagonal and 0’s off the diagonal.

**Zero matrix:**

Any matrix (of any type), with only zero entries.

**Definition of a 2-dimensional matrix:**

We define of a 2-dimensional matrix as: .

**Definition of the rank of a matrix:**

The rank of a matrix A is the greatest n such that A has a square sub-matrix of type nxn with determinant not equal to zero.

**Definition of an invertible matrix:**

We say a square matrix A is invertible if there exits a (square) matrix B such that AB=BA=identity matrix.

**Cramer’s Rule:**

If A is a square matrix, then the equation AV=w has a unique solution if and only if and the solution is.