| Description |
Linear maps, change of basis, normal form of a linear map, dimension formula,
problem of choice of basis for an endomorphism, invariant subspaces, eigenvalues and eigenvectors, diagonalizabilizy, characteristic polynomial, minimal polynomial of a vector wrt an endomorphism, Caley-Hamilton, minimal polynomial of an endomorphism, Jordan normal form for endomorphisms whose minimal polynomial
splits in linear factors,
Isometries of Rn, rotations of R2 and R3 and orthogonal matrices, linear systems of ODE's with constant coefficients, exponential map for complex matrices,
bilinear forms, symmetric bilinear forms, Gram-Schmid Orthogonalization, orthogonal basis for real symmetric bilinear forms, Sylvesters theorem, spectral theorems for hermitian and normal endomorphisms, symplectic forms, conic sections, principal axis theorem, proof of the friendship theorem |
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