advanced-linear-algebra

Every operator on a complex space has an eigenvalue

taught

Unlike a real operator, which can rotate every vector off its own span, an operator on a nonzero finite-dimensional complex space is guaranteed at least one eigenvalue.

Taught in

Every operator on a complex space has an eigenvalue
Advanced Linear Algebra

Requires

eigenvalues-and-the-characteristic-equation required
complex-arithmetic-for-linear-algebra required

Required by

Invariant subspaces and upper-triangular form required
Self-adjoint operators and real eigenvalues required

Local knowledge map

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