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360 Sysquake User Manual ©1999-2012, Calerga Sàrl Description pinv(M1) returns the pseudo-inverse of matrix M. For a nonsingular square matrix, the pseudo-inverse is the same as the inverse. For an arbitrary matrix (possibly nonsquare), the pseudo-inverse M2 has the following properties: size(M2) = size(M1’), M1*M2*M1 = M1, M2*M1*M2 = M2, and the norm of M2 is minimum. The pseudo-inverse is based on the singular-value decomposition, where only the singular values larger than some small threshold are considered. This threshold can be specified with an optional second argument tol or as a named argument. If M1 is a full-rank matrix with more rows than columns, pinv returns the least-square solution pinv(M1)*y = (M1’*M1)\M1’*y of the overdetermined system M1*x = y. Examples pinv([1,2;3,4]) -2 1 1.5 -0.5 M2 = pinv([1;2]) M2 = 0.2 0.4 [1;2] * M2 * [1;2] 1 2 M2 * [1;2] * M2 0.2 0.4 See also inv, svd poly Characteristic polynomial of a square matrix or polynomial coefficients based on its roots. Syntax pol = poly(M) pol = poly(r) Description With a matrix argument, poly(M) returns the characteristic polynomial det(x*eye(size(M))-M) of the square matrix M. The roots of the characteristic polynomial are the eigenvalues of M.
