Eigenvalue Calculator of a matrix | Tool for Eigenvalues

Make use of this simple and straightforward calculator that offers the eigenvalues for a matrix. Eigenvalue Calculator takes the numbers i.e matrix in the input fields and generates the output in less amount of time by hitting the calculate button provided beside the input box.

Eigenvalue Calculator: Are you struggling to get the eigenvalues for matrix? Then, try this handy calculator tool and make your mathematical calculations immediately and easily. This calculator gives the detailed process of obtaining a solution to your question and the direct answer within fraction of seconds. We are also providing the examples, which are helpful to check whether the result is correct or not.

Simple Method To Find Eigenvalues

One of the best and shortest methods to calculate the Eigenvalues of a matrix is provided here. Checkout the simple steps of Eigenvalue Calculator and get your result by following them.




  • Take proper input values and represent it as a matrix.
  • Frame a new matrix by multiplying the Identity matrix contains v in place of 1 with the input matrix.
  • Find the determinant of the obtained matrix i.e multiplication of the diagonal values of a matrix and subtract the results.
  • The above process will form a characteristic polynomial.
  • Solve the equation to get the roots.
  • The obtained roots are eigenvalues for your input matrix.

Example:

 

Question: Find the eigenvalues of a matrix ((-2,-4,2),(-2,1,2),(4,2,5))?

 

Solution:

Given matrix A= [(-2,-4,2),(-2,1,2),(4,2,5)]

To get the characteristic equation of matrix A, make

A-VI=0, where I is an Identity matrix.

Matrix=[(-2,-4,2),(-2,1,2),(4,2,5)]*[(v,0,0),(0,v,0),(0,0,v)]

Matrix=[(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]

Det Matrix=0

Det [(-2-v,-4,2),(-2,1-v,2),(4,2,5-v)]= 0

By expanding the determinant:

(-2-v)x[(1-v)x(5-v)-2×2]+4[(-2)x(5-v)-4×2]+2[(-2)x2-4(1-v)]=0

After simplifying

-v3+4v2+27v-90=0

or v3-4v2-27v+90=0

By applying trial and error method, we got

v3-4v2-27v+90=(v-3)(v2-v-30)

(v-3)(v2-v-30)=(v-3)(v+5)(v-6)

That means eigenvalues are 3,-5,6

FAQs on Eigenvalue Calculator

1. Does every matrix have eigenvalues?

Every matrix has an eigenvalue, but it may be a complex number.


2. What does a zero eigenvalue means?

Geometrically, zero eigenvalue means no information in an axis. We all know that the determinant of a matrix is equal to the products of all eigenvalues. If one or more eigenvalues are zero then the determinant is zero and which is a singular matrix.


3. Are eigenvalues unique?

Eigenvalues are not unique.


4. What is the eigenvalue of a matrix?

Eigenvalues are the special set of scalars associated with a linear system of equations known as characteristic roots and values.


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