Matrix
Eigenvalue Calculator
Find eigenvalues and eigenvectors for matrices. Compute the characteristic polynomial, eigenvalues, and eigenvectors of square matrices for linear algebra analysis.
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Solution Methodology
01
Create Characteristic Matrix
Subtract λ from the diagonal elements of the matrix.
02
Find Determinant
Set the determinant of the characteristic matrix to zero to form the characteristic polynomial.
03
Solve for Eigenvalues
Find the roots of the polynomial (λ) and then solve for eigenvectors.
Common Questions
What are eigenvalues and eigenvectors?
An eigenvector is a non-zero vector that changes only in scale (not direction) when a linear transformation (matrix A) is applied to it. The scale factor is the eigenvalue. Mathematically, Av = λv.
How do you find the characteristic equation?
The characteristic equation is found by subtracting λ from the main diagonal of the matrix A (giving A - λI), calculating the determinant of that new matrix, and setting it to zero.