Types of Matrices

Row Matrix

A row matrix is formed by a single row.

Row Matrix

Column Matrix

A column matrix is formed by a single column.

Column Matrix

Rectangular Matrix

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

Rectangular Matrix

Square Matrix

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

The elements of the form aii constitute the principal diagonal.

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

Square Matrix

Zero Matrix

In a zero matrix, all the elements are zeros.

Zero Matrix

Upper Triangular Matrix

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

Upper Triangular Matrix

Lower Triangular Matrix

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

Lower Triangular Matrix

Diagonal Matrix

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

Diagonal Matrix

Scalar Matrix

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

Scalar Matrix

Identity Matrix

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

Identity Matrix

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.

Transpose Matrix

(At)t = A

(A + B)t = At + Bt

(α ·A)t = α · At

(A · B)t = Bt · At

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:

A2 = A.

Involutive Matrix

The matrix A is involutive if:

A2 = I.

Symmetric Matrix

A symmetric matrix is a square matrix that verifies:

A = At.

Antisymmetric Matrix

An antisymmetric matrix is a square matrix that verifies:

A = −At.

Orthogonal Matrix

A matrix is orthogonal if it verifies that:

A · At = I.