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Some useful linear algebra
Linearly independent vectors span(V): span of vector space V is all linear combinations of vectors v i, i.e.
The eigenvalues of A are the roots of the characteristic equation Eigenvectors of A are columns of S diagonal form of matrix
Similarity transform then A and B have the same eigenvalues The eigenvector x of A corresponds to the eigenvector M -1 x of B
Rank and Nullspace
Least Squares More equations than unknowns Look for solution which minimizes ||Ax-b|| = (Ax-b) T (Ax-b) Solve Same as the solution to LS solution
Properties of SVD Columns of U (u 1, u 2, u 3 ) are eigenvectors of AA T Columns of V (v 1, v 2, v 3 ) are eigenvectors of A T A 2 are eigenvalues of A T A
with equal to for all nonzero singular values and zero otherwise pseudoinverse of A Solving
Least squares solution of homogeneous equation Ax=0
Enforce orthonormality constraints on an estimated rotation matrix R’
Newton iteration measurement parameter f( ) is nonlinear
Levenberg Marquardt iteration
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Matrices CS485/685 Computer Vision Dr. George Bebis.
Linear Algebra Review By Tim K. Marks UCSD Borrows heavily from: Jana Kosecka Virginia de Sa (UCSD) Cogsci 108F Linear.
Introduction The central problems of Linear Algebra are to study the properties of matrices and to investigate the solutions of systems of linear equations.
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