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VECTOR SPACES y
MATRICES AND SYSTEMS OF LINEAR
9 other sections not shown
algebra arbitrary called coefficients column vectors complex numbers coordinate axes coordinate system coordinate vector Corollary curve cylinder defined denoted diagonal elements diagonal matrix diagonalizable dimension eigenvalues eigenvectors ellipse equivalent Example Exercise F-basis finite dimensional follows Fu F2 graph Hence Hermitian hyperboloid initial point inner product space intersection inverse isomorphism linear combination linear transformation linearly independent m x n mapping mutually orthogonal n x n matrix nonsingular matrix nontrivial linear relation nonzero vector null space one-to-one orthogonal matrix orthonormal basis P~lAP parallel parallelogram permutation perpendicular plane polynomials positive definite Problem Proof Prove quadratic form quadric rank real numbers relative satisfy scalar multiple Section set of vectors solution space solution vector space spanned standard basis subspace surface symmetric symmetric matrix terminal point Theorem three vectors transition matrix unit vectors unitary unitary matrix unitary space V1 and V2 vector space XTAX xy-plane zero vector