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Length of a Vector
Addition of Vectors Linear Combinations
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angle apup augmented matrix axis Chapter coefficient matrix combination of Ui complex numbers components Compute coordinate system corresponding cross product defined definition denote det(u determinant diagonal entries diagonal matrix diagonalizable dimension dot product echelon form eigenvalues eigenvectors eigenvectors belonging equal equivalent Example Find a vector formula function from Rn geometric Gram-Schmidt process graph gth column Hence homogeneous system identity matrix implies independent set invertible kernel length linear combination linear equations linear function linear mapping mapping from Rn n-tuple orthogonal mapping orthogonal matrix parallel position vectors proof prove pth row quadratic form rank real numbers Rn to Rn rotation row space satisfying scalar multiples Section set of vectors Similarly solutions space spanned spanning set subspace of Rn symmetric system of equations tail Theorem tion us+i vector perpendicular vector space vectors in Rn z-axis