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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.

### 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 eigenvector $$v$$ 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 eigenvector. Use the eigenvectors calculator proposed by dCode.

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

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

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

For example, the eigenvector associated to 5 is $$\begin{bmatrix} 1 \\ 2 \end{bmatrix}$$.