# Eigenvalue Calculator

## Related Converters

An eigenvalue calculator is a dynamic tool that displays the eigenvalue for a given matrix. Our eigenvalue finder is designed with user needs in mind to provide precise and fast calculations.

## Concept of Eigenvalue in Matrix:

“The set of values for which a different equation has a non-zero solution under a given condition is known as the eigenvalue”.

This term is associated with the set of linear equations of a 2x2, 3x3, or higher-order square matrix. It is such a factor by which an engine vector is stretched and if the value is negative then it will be reversed.

## Evaluation Formula:

The scalar value like square matrix and nonzero vectors is associated with the system of linear equations multiplied, then the result is a scaled version of V and λ. In the formulaic term, the linear transformation corresponds to the matrices given below:

$$Av \;=\; λv$$

In order to find eigenvalues the above can be rewritten as follows:

$$(A \;-\; λI)v \;=\; 0$$

This formula is used by the eigenvalues calculator in which:

• I indicate the identity matrix
• A shows the scalar matrix
• V is a nonzero vector

## Calculate Eigenvalues of a Matrix:

Eigenvalue has a key role in the linear algebra. The eigenvalues calculator finding eigenvalues of a given square matrix with steps. You are curious about how to find eigenvalues of 3x3 matrix so look at the example:

### Example:

Suppose a special set of square matrix $$\left[\begin{matrix}2 & 1\\2 & 3 \end{matrix}\right]$$

#### Solution:

Step # 1:

Subtract λ from the diagonal entries of the given matrix

$$\left[\begin{matrix}2.0 - \lambda & 1.0\\2.0 & 3.0 - \lambda\end{matrix}\right]$$

Step # 2:

Cross-multiply the matrix values together to get the eigenvalue or directly use the matrix eigenvalue calculator 3x3.

( 2 - λ ) ( 3 - λ ) - ( 1 ) ( 2 )

6 - 2λ - 3λ + λ^2 - 2

6 - 5λ + λ^2 - 2

Step # 3:

The determinant of the obtained matrix

λ^2 - 5λ + 4 = 0

λ^2 - 4λ - λ + 4 = 0

λ ( λ - 4 ) - 1 ( λ - 4 ) = 0

( λ - 4 ) ( λ - 1)

So the roots of the Eigenvalue that is evaluated by the given matrix are as follows:

λ1 = 4
λ2 = 1

## Working of EigenValue Calculator:

Our eigen value calculator works for eigenvalues of a 3x3 matrix and determines the complex calculations within a second by taking into service the below points:

Input:

• Set the number of matrices
• Put the values according to the selection
• Tap the “Calculate” button

Output:

Our online eigenvalue calculator 3x3 responds you the below values when you put the above values in their designated fields.

• Eigenvalues for a given matrices
• Step-by-step calculations

## Common Questions:

### Can Eigenvalue Be Used for Non-Square Matrices?

Eigenvalues are only associated with square matrices and this term is not used for non-square matrices.

### Can Eigenvalue Be Infinitive?

No, it is not possible! If it is possible then there is a column vector.

### What Are The Types of Eigenvalues?

There are the following types that are as follows:

• One Eigenvalue
• Two distinct real values
• Complex conjugate

## Citation:

Wikipedia: Eigenvalues and eigenvectors, Formal definition, Eigenvalues and eigenfunctions of differential operators.

Libre Text: Eigenvalues and Eigenvectors, An eigenvector with eigenvalue 0, Reflection, Dilation, Shear, Rotation, Eigenvectors with Distinct Eigenvalues are Linearly Independent