# Matrix Power Calculator

## Raise a matrix to an integer power step by step

The calculator will find the given matrix raised to the given integer (positive or negative) power (if possible), with steps shown. Thus, it can square and cube the matrix. It handles matrices of any size up to 7x7 (2x2, 3x3, 4x4, etc.).

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

The Matrix Power Calculator is a powerful online tool that enables you to swiftly and precisely compute the power of a matrix. In the realm of linear algebra, calculating the power of a matrix entails repeatedly multiplying the matrix by itself. Whether you're a student, teacher, engineer, or scientist dealing with square matrices, our calculator has got you covered.

## How to Use the Matrix Power Calculator?

Using our matrix power calculator is a breeze. Follow these simple steps:

• ### Square Matrix

Start by entering the elements of your square matrix into the provided fields. Remember, only square matrices (matrices with the same number of rows and columns) can be raised to a power.

• ### Power Value

Next, input the power to which you want to raise the matrix.

• ### Calculate

Click on the "Calculate" button. Our calculator will quickly process your input and display the matrix power in the results section.

## What Is a Matrix?

A matrix is a rectangular array of numbers arranged in rows and columns. The numbers in the matrix are called its elements or entries. Matrices are a fundamental concept in linear algebra and are used across many fields including physics, computer science, statistics, and economics. They serve as a compact way to represent and work with sets of linear equations or transformations.

The size or dimensions of a matrix are defined by the number of rows and columns it has. A matrix with $m$ rows and $n$ columns is called an $m$ by $n$ matrix, often written as $m\times n$.

For instance, here is a 2x3 matrix (2 rows, 3 columns):

$$\left[\begin{array}{ccc}1&2&3\\4&5&6\end{array}\right]$$

A special type of matrix, called a square matrix, has an equal number of rows and columns. Some operations, such as finding the determinant or calculating the power of a matrix, can only be performed on square matrices.

## What Is Matrix Power?

Matrix power refers to the result derived from repeatedly multiplying a square matrix by itself for a specified number of times. As an example, if we have a square matrix $A$, its square (denoted as $A^2$) is obtained when matrix $A$ is multiplied by itself.

It's crucial to remember that matrix power operations can only be performed on square matrices, i.e., matrices with equal numbers of rows and columns. Moreover, if the matrix is diagonalizable, it is better to diagonalize it first and then raise it to a power in order to reduce the calculations.

## Calculating Matrix Power

The process of calculating matrix power can be straightforward for smaller powers where manual multiplication is feasible. However, for larger powers, this can be a tedious and error-prone task. That's where our Matrix Power Calculator comes in handy. It performs the repetitive multiplication quickly and accurately, saving you time and effort.

Here's the formula for calculating the square of a matrix $A$:

$$A^2=A\cdot A$$

Moreover, the formula for calculating the cube of a matrix $A$ is

$$A^3=A\cdot A\cdot A$$

And so forth for higher powers.

For example, suppose we have a 2x2 square matrix $A=\left[\begin{array}{cc}2&3\\1&4\end{array}\right]$ and we want to calculate $A^3$.

Input these values into their respective fields and click "Calculate." The result will be a new 2x2 matrix that is the cube of the matrix $A$.

Our matrix power calculator offers a seamless and intuitive way to calculate matrix power. Give it a try today!

## Why Choose Our Matrix Power Calculator?

• ### Efficient

It makes calculating the matrix power a quick and simple process.

• ### Accurate

This tool guarantees precise results, reducing the chances of errors that can occur with manual calculations.

• ### Versatile

It can handle square matrices of various dimensions.

• ### Free

Our matrix power calculator is 100% free to use.

• ### User-Friendly

With a clean, intuitive interface, our calculator is easy to use for everyone, regardless of your level of mathematical proficiency.

### FAQ

#### Is the Matrix Power Calculator accurate?

Yes, our Matrix Power Calculator provides highly accurate results, eliminating the possibility of manual calculation errors, especially for large power values or matrices.

#### Can I calculate the power of non-square matrices with this calculator?

No, matrix power calculations are only defined for square matrices, i.e., those with an equal number of rows and columns. Non-square matrices cannot be raised to a power.

#### How does the Matrix Power Calculator work?

The Matrix Power Calculator automates the multiplication process involved in raising a matrix to a power. It multiplies the input matrix by itself for the number of times specified by the power value.