Examples for

# Matrices

A matrix is a two-dimensional array of values that is often used to represent a linear transformation or a system of equations. Matrices have many interesting properties and are the core mathematical concept found in linear algebra and are also used in most scientific fields. Matrix algebra, arithmetic and transformations are just a few of the many matrix operations at which Wolfram|Alpha excels.

### Matrix Properties

Explore various properties of a given matrix.

### Trace

Calculate the trace or the sum of terms on the main diagonal of a matrix.

### Row Reduction

Reduce a matrix to its reduced row echelon form.

### Diagonalization

Find the diagonalization of a square matrix.

### Types of Matrices

Find information on many different kinds of matrices.

### Matrix Arithmetic

Add, subtract and multiply vectors and matrices.

### Determinant

Calculate the determinant of a square matrix.

### Eigenvalues & Eigenvectors

Calculate the eigensystem of a given matrix.

#### Compute the characteristic polynomial of a matrix:

Matrix Decompositions

Transform a matrix into a specified decomposition.

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### GO FURTHER

Step-by-Step Solutions for Linear Algebra

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Free Unlimited Linear Algebra Practice Problems

### RELATED EXAMPLES

• Algebra
• Equation Solving
• Linear Algebra
• Vector Analysis
• Vectors
• ### Inverse

Invert a square invertible matrix or find the pseudoinverse of a non-square matrix.

### Other Matrix Operations

Perform various operations, such as conjugate transposition, on matrices.

#### Compute the adjugate of a matrix:

Geometric Transformations

Find matrix representations for geometric transformations.

#### Compute a 3 x 3 reflection matrix:

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