Eigenvalue

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An eigenvalue of a square matrix <math>A</math> is a complex number <math>\lambda</math> such that

<math>A\boldsymbol{x}=\lambda\boldsymbol{x}</math>

for some non-zero vector <math>\boldsymbol{x}\in\mathbb{R}</math> known as a eigenvector. The eigenvalue is the zero of a matrix's charateristic polynomial.

The span of all the eigenvectors corresponding to a fixed eigenvalue <math>\lambda</math> is called the eigenspace <math>E_\lambda</math> of <math>A</math>.