# Types of Matrices

#### Row Matrix

A row matrix is formed by a single row.

#### Column Matrix

A column matrix is formed by a single column.

#### Rectangular Matrix

A rectangular matrix is formed by a different number of rows and columns, and its dimension is noted as:** mxn**.

#### Square Matrix

A square matrix is formed by the same number of rows and columns.

The elements of the form **a _{ii}** constitute the principal diagonal.

The secondary diagonal is formed by the elements with **i+j = n+1**.

#### Zero Matrix

In a zero matrix, all the elements are zeros.

#### Upper Triangular Matrix

In an upper triangular matrix, the elements located below the diagonal are zeros.

#### Lower Triangular Matrix

In a lower triangular matrix, the elements above the diagonal are zeros.

#### Diagonal Matrix

In a diagonal matrix, all the elements above and below the diagonal are zeros.

#### Scalar Matrix

A scalar matrix is a diagonal matrix in which the diagonal elements are equal.

#### Identity Matrix

An identity matrix is a diagonal matrix in which the diagonal elements are equal to 1.

#### Transpose Matrix

Given matrix A, the transpose of matrix A is another matrix where the elements in the columns and rows have switched. In other words, the rows become the columns and the columns become the rows.

**(A ^{t})^{t} = A**

**(A + B) ^{t} = A^{t} + B^{t}**

**(α ·A) ^{t} = α · A^{t}**

**(A · B) ^{t} = B^{t} · A^{t}**

#### Regular Matrix

A regular matrix is a square matrix that has an inverse.

#### Singular Matrix

A singular matrix is a square matrix that has no inverse.

#### Idempotent Matrix

The matrix A is idempotent if:

**A ^{2} = A**.

#### Involutive Matrix

The matrix A is involutive if:

**A ^{2} = I**.

#### Symmetric Matrix

A symmetric matrix is a square matrix that verifies:

**A = A ^{t}**.

#### Antisymmetric Matrix

An antisymmetric matrix is a square matrix that verifies:

**A = −A ^{t}**.

#### Orthogonal Matrix

A matrix is orthogonal if it verifies that:

**A · A ^{t} = I.**