Eigenvalue Calculator

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.