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Eigenvalues of a Matrix

Tool to calculate eigenvalues of a matrix. The eigenvalues of a matrix are values that allow to reduce the associated endomorphisms.

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Eigenvalues of a Matrix -

Tag(s) : Mathematics,Algebra,Symbolic Computation

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Eigenvalues of a Matrix

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Eigenvalues Calculator

Tool to calculate eigenvalues of a matrix. The eigenvalues of a matrix are values that allow to reduce the associated endomorphisms.

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How to calculate eigen values of a matrix?

Consider \( M \) a square matrix, the eigenvalues of M are the roots of the characteristic polynomial \( P \) of the matrix M.

Eigenvalues are generally called \( \lambda \) associated with the eigenvectorhref \( v \) if $$ M.v = \lambda v \iff (M-\lambda I) v = 0 $$ with \( I \) the identity matrix.

An eigenvalue of a matrix is always associated with an eigenvectorhref. Use the eigenvectorshref calculator proposed by dCode.

$$ M=\begin{pmatrix} 1 & 2 \\ 4 & 3 \end{pmatrix} \Rightarrow P(M)=x^2−4x−5=(x+1)(x-5)$$

$$ P(M)=0 \iff x= -1 \mbox{ or } x = 5 $$

The eigenvalues of the matrix M are -1 and 5.

For example, the eigenvectorhref associated to 5 is \( \begin{pmatrix} 1 \\ 2 \end{pmatrix} \).

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