An introduction to linear algebra
Vector spaces; Linear combinations; Dimension basis; Linear functionals and linear equations; Linear equations, abstractly; Matrices; Determinants; Linear transformations; Eigenvectors eigenvalues; Minimum polynomial: jordan form; Quadratic form; Inner products; The spectral theorem.
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abstract axes bases bilinear called Chapter characteristic polynomial coefficients column vectors column-echelon form complex numbers components compute consider coordinates corresponding course defined denoted dependent determine diagonal diagonalizable dimension direct sum eigenspace eigenvalues eigenvectors entries equal example fact factor form a basis formula geometric given Hermitean independent intersection inverse Jordan form kernel kerT linear algebra linear combination linear equations linear functional linear transformation linear variety means multiple negative nilpotent nonzero Note notion operator orthogonal orthogonal matrix plane positive definite Problem PROOF Proposition quadratic form quadric rank rank-nullity reduces relation representing respect rotation row vector row-echelon form satisfies scalar Section Show similarly simply solution space solve span spectral theorem square standard inner product subspace sum-of-squares Suppose symmetric T-image T-invariant transition matrix transpose triangular unique unitary variables vector space write written X'AX