Introduction to Eigenvalue Calculator:
The eigenvalue calculator is an online tool that helps you to find eigenvalues for the given matrices in less than a minute. It is used to evaluate the matrix eigenvalues with the help of the determinant method and a square matrix which is multiple of a scalar.
Although the eigenvalue method is not too complex, it becomes a headache for so many students because they are not aware of the basics of matrices and linear transformations. To get rid of this problem we introduce our eigenvalues calculator that can easily give you solutions to your matrices problems instantly.
What is Eigenvalue?
Eigenvalue is an important concept in linear algebra in which a square matrix is associated with a scalar for the conversion of characteristic equations to find scalar(eigenvalue) values in the given matrix.
This method is used in various fields such as physics, engineering, computer science, and more. For a given square matrix A, an eigenvector v is a non-zero vector, and a scalar λ is a multiple of A. The scalar is known as the eigenvalue. Mathematically, it is expressed as:
$$ det(λI - A \;=\; 0 $$
I is the identity matrix.
After calculation, the eigen value calculator solves the equation using the values you provide and then gives the exact value.
How to Find the Eigenvalues of a Matrix?
To calculate eigenvalues of a square matrix A, first, the eigenvalue calculator converts the given matrix into a characteristic equation for the solution of eigenvalues. The step-by-step calculation process of eigenvalues is given below.
Example:
Find the eigenvalues of the following,
$$ A \;=\; \biggr[\begin{matrix} -5 & 2 \\ -7 & 4 \\ \end{matrix} \biggr] $$
Solution:
Steps to Find Eigenvalues
To find the wigen value of a matric A, the eigen values of a matrix calculator first converts this matrix into a characteristic equation with the help of determinant as:
$$ det(λI - A) \;=\; 0 $$
Put the value of matrix A, I is an identity matrix as per the order of A matrix(2 by 2) to find the determinant matrix.
$$ det \biggr(λ \biggr[\begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \biggr] - \biggr[\begin{matrix} -5 & 2 \\ -7 & 4 \\ \end{matrix} \biggr] \biggr) \;=\; 0 $$
Solve this matrix with the help of matrix rules of linear transformation such as:
$$ det \biggr[\begin{matrix} λ + 5 & -2 \\ 7 & λ - 4 \\ \end{matrix} \biggr] \;=\; 0 $$
After solving the determinant, you get a quadratic equation from the characteristic equation.
$$ λ^2 + λ - 6 \;=\; 0 $$
Solve this equation with the help of the factorization method.
$$ λ^2 + 3λ - 2 λ - 6 \;=\; 0 $$
$$ λ(λ + 3) - 2(λ + 3) \;=\; 0 $$
$$ (\lambda + 3) \; (\lambda - 2) \;=\; 0 $$
$$ (λ + 3) \;=\; 0 \; , \; (λ - 2) \;=\; 0 $$
$$ λ \;=\; -3 \; , \; λ \;=\; 2 $$
The eigenvalues of the given matrix A of 2 by 2 order is λ= -3, λ= 2.
In the same way, the eigenvalue finder uses this method for solving eigenvalues for 3 by 3 or 4 by 4 order of matrix.
How to Use the Eigenvalue Calculator?
The eigenvalues calculator has an easy-to-use interface you don't need to become an expert. You just need to enter your problem of matrices to find its eigenvalues and get a solution in a simplified method. Follow our guidelines before using it because it is very helpful for you. These guidelines are:
- Select the matrix size (2 by 2 or maybe 3 by 3) from the given list.
- Enter the elements of the given matrix in the next input box.
- Review the given matrix value before hitting the calculate button to start the evaluation process in the eigen value calculator.
- Click the “Calculate” button to get the solution of your given matrix problem for eigenvalue.
- If you are trying out our eigen values of a matrix calculator for the first time then you must use the load example to learn more about eigenvalue calculations.
- Click on the “Recalculate” button to get a new page for finding more example solutions of eigenvalues problems.
Final Result of Eigenvalues Calculator:
The eigen value calculator gives you the solution to a given matrix question when you add the input into it. It provides you with solutions of eigenvalues. It may be included as:
- Result option
When you click on the result option the eigenvalue calculator gives you a solution of matrix eigenvalue.
- Possible steps
It provides you with a solution where all the calculations of square matrix steps are mentioned, just click on this option.
Benefits of Using Eigen Value Calculator:
The eigenvalue finder provides several benefits whenever you use it to calculate the matrices problems and provides eigenvalues in solutions immediately. These benefits are:
- The eigen values of a matrix calculator is a free-of-cost tool that enables you to use it for free to find the matrix problem solution without any fee.
- It is an adaptable tool that can solve various orders of matrices to find the eigenvalue solution.
- Our eigenvalues calculator helps you to get a strong hold on the Eigenvalue method concept for matrix when you use it for practice by solving more examples.
- It saves the time that you consume on the calculation of eigenvalues in a couple of minutes.
- It is a reliable tool that provides accurate solutions whenever you use it to calculate the eigenvalue of the matrix without any error.
- Eigenvalue Calculator provides the solution without giving conditions which means you can use it multiple times, whenever you use it.
