Find Characteristic Polynomial, Eigenvalues and Eigenvectors of a square Matrix
Characteristic Polynomial of the square n × n matrix A , denoted by pA (λ), is defined as a determinant of λI - A,
where I is the n × n identity matrix.
Roots λi (i = 1,...,n) of the characteristic polinomial pA (λ) of the matrix A are the eigenvalues of A.
If the matrix A is considered as a linear transformation T : ℝn → ℝn, then, eigenvector (characteristic vector) of a matrix A is the
nonzero vector vi ∈ ℝn, such that it changes by the linear transformation T by at most the scalar factor λi which is one of the eigenvalues of the matrix A.
To find Characteristic Polynomial, Eigenvalues and Eigenvectors, first, specify the dimension n of the matrix A, and then populate the matrix.
Please note:
Dimension of the matrix :
Characteristic Polynomial of the square n × n matrix A , denoted by pA (λ), is defined as a determinant of λI - A,
where I is the n × n identity matrix.
Roots λi (i = 1,...,n) of the characteristic polinomial pA (λ) of the matrix A are the eigenvalues of A.
If the matrix A is considered as a linear transformation T : ℝn → ℝn, then, eigenvector (characteristic vector) of a matrix A is the
nonzero vector vi ∈ ℝn, such that it changes by the linear transformation T by at most the scalar factor λi which is one of the eigenvalues of the matrix A.
To find Characteristic Polynomial, Eigenvalues and Eigenvectors, first, specify the dimension n of the matrix A, and then populate the matrix.
Please note:
- We have limited the dimension n in the "Manual Entry" tab to 10 due to the limited space on the screen. For higher dimensions, please use "File Upload" tab.
- For the matrices dimension 3 or less, eigenvalues will be calculated analytically. However, for dimensions 4 and greater,
we might need to use the numerical methods to find eigenvalues. - Some authors are deifining charcteristic polinomial as det(A - λI) , however, we are using the det (λI - A) form which will give a monic polinomial.
A =
We are working hard to finish it, and you will be able to use it soon.
