Editing Complex number (section)

=== Linear algebra ===
Since <math>\C</math> is algebraically closed, any non-empty complex [[square matrix]] has at least one (complex) [[eigenvalue]]. By comparison, real matrices do not always have real eigenvalues, for example [[rotation matrix|rotation matrices]] (for rotations of the plane for angles other than 0° or 180°) leave no direction fixed, and therefore do not have any ''real'' eigenvalue. The existence of (complex) eigenvalues, and the ensuing existence of [[Eigendecomposition of a matrix|eigendecomposition]] is a useful tool for computing matrix powers and [[matrix exponential]]s. 

Complex numbers often generalize concepts originally conceived in the real numbers. For example, the [[conjugate transpose]] generalizes the [[transpose]], [[Hermitian matrix|hermitian matrices]] generalize [[Symmetric matrix|symmetric matrices]], and [[Unitary matrix|unitary matrices]] generalize [[Orthogonal matrix|orthogonal matrices]].