Applied Linear Algebra
Contains important modern applications such as signal processing and Karmarkar's approach to linear programming. Uses Gauss reduction and 'Gauss-reduced form' as the fundamental theoretical and computational tool. Includes examples and problems using modern software for matrix computations, and describes properties and sources of software for real applied problems. Stresses both the theoretical and practical importance of tools such as the singular-value decomposition and generalized (pseudo) inverses, the QR decomposition, Householder transformations/matrices, and orthogonal projections. Features 1,100 exercises, including optional computer examples and problems.
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SOME SIMPLE APPLICATIONS AND QUESTIONS
SOLVING EQUATIONS AND FINDING INVERSES METHODS
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a p x p able to solve applied arithmetic augmented matrix basic feasible vector bottom row Chapter coefficients column matrix compute Consider constraints converges Corollary defined denote det(A determine dual eigensystems eigenvalues eigenvectors eigenvectors associated equal zero equivalent Example Gauss elimination Gauss-Jordan elimination Gauss-reduced form geometrical vectors hermitian inner product interchanges inverse Jordan form Key Theorem leading columns least-squares problem left-inverse linear combination linear equations linear program linear transformation linearly independent linearly independent set main diagonal main-diagonal entries MATLAB or similar maximize minimize nonnegative nonsingular matrix norm null space obtain optimal ordered basis orthonormal p x p matrix p x q pivot proof quadratic form rank result right-inverse row-echelon form satisfying scalars Section Show similar software simplex method singular value decomposition solve Problems spanning set Suppose symmetric matrix system of equations tableau unitary unitary matrix upper-triangular variables vector space verify