LACS.PAR.7

LACS.PAR.7

LACS.PAR.7.1Determine whether a given set of vectors generates a vector space.LACS.PAR.7.10Find an orthogonal basis for a given basis or subspace by applying the Gram-Schmidt orthonormalization process.LACS.PAR.7.11Perform QR factorization of a matrix to solve matrix equations.LACS.PAR.7.12Apply the method of least squares to find the line or parabola of best fit to approximate data in context.LACS.PAR.7.13Apply the grow-and-shrink algorithm in the minimum spanning forest problem in GF(2).LACS.PAR.7.14Apply the Exchange Lemma to image perspective rendering.LACS.PAR.7.15Use bases to represent images and sounds as wavelets; perform wavelet transformation, implementation, and decomposition through programming.LACS.PAR.7.16Program a Fast Fourier Transform to store a sequence of amplitude samples.LACS.PAR.7.17Apply the Rank Theorem to demonstrate the simple authentication scheme.LACS.PAR.7.2Justify whether a subset of a vector space is a subspace.LACS.PAR.7.3Determine whether a given vector is in the linear span of a set of vectors.LACS.PAR.7.4Determine whether two vector subspaces are orthogonal; find the orthogonal component of a given subspace.LACS.PAR.7.5Determine whether a set of vectors is a basis for a vector space.LACS.PAR.7.6Find the dimension of a vector space; find the dimensions of the row space, column space, and kernel for a given matrix; find the rank of a matrix.LACS.PAR.7.7Find a matrix representing a linear map.LACS.PAR.7.8Determine the change of representation for a linear transformation given two different bases on a vector space.LACS.PAR.7.9Determine if two matrices are similar; determine if two matrices are orthogonal.
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