MATRIX ALG STAT COMPU
MATRIX ALG STAT COMPU STA 6329
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This 1 page Study Guide was uploaded by Golden Bernhard on Friday September 18, 2015. The Study Guide belongs to STA 6329 at University of Florida taught by Mark Yang in Fall. Since its upload, it has received 35 views. For similar materials see /class/206565/sta-6329-university-of-florida in Statistics at University of Florida.
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Date Created: 09/18/15
Review for the Final Dec 15 Monday 121302130 closed book Coverage Chapters 127 137 147 and 21 only lectured materials will be cov ered Simple SAS questions A Memorize the following de nitions A1 Elementary row column operations and their matrix representation from lecture A2 Rank and trace of a matrix A3 Linear space7 subspace7 basis7 and orthogonal basis A4 lnner product and Gram Schmidt orthogonalization algorithm A5 lnverse7 Left inverse7 right inverse and generalized inverse including the simple form and Moore Penrose unique representation A6 Projection on a subspace A7 De nition of the determinant of a square matrix A8 Positive definite7 nnd matrices A9 Eigenvalues and eigenvectors A10 Similar matrices B Memorize the following facts or key theorems and can nish the proof with hints from de nition to nish 131 Construction of the projection matrix 123 B2 Theorem 1326 Exchange of rows changes signs of a determinant 133 Lemma 1329 Adding a row to another row will not change the value of a determi nant 134 Theorem 1334 AB and its proof 135 Eigenvectors are independent for different eigenvalues 136 Corollary 2153 Necessary and suf cient condition for diagonalization 137 Theorem 2157 diagonalization of the symmetric matrix 138 Theorem 21121 singular value decomposition C Things to review C1 Exercise 8 12 C2 Applications of diagonalization from lecture C3 Application of SVD C4 Cofactors and adjoint
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