If A is a 378-by-1 matrix and B is a 378-by-2401 matrix, what does is it mean 'A\B'?

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Wanda Love
Wanda Love 2015-5-22
回答： Rushikesh Tade 2015-5-22
If A is a 378-by-1 matrix and B is a 378-by-2401 matrix, what does is it mean 'A\B'? what is the algorithm used in MATLAB? Thx.

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Rushikesh Tade
Rushikesh Tade 2015-5-22
Ref from http://dali.feld.cvut.cz/ucebna/matlab/techdoc/ref/arithmeticoperators.html
Backslash or matrix left division. If A is a square matrix, A\B is roughly the same as inv(A)*B, except it is computed in a different way. If A is an n-by-n matrix and B is a column vector with n components, or a matrix with several such columns, then X = A\B is the solution to the equation AX = B computed by Gaussian elimination (see "Algorithm" for details). A warning message prints if A is badly scaled or nearly singular. If A is an m-by-n matrix with m ~= n and B is a column vector with m components, or a matrix with several such columns, then X = A\B is the solution in the least squares sense to the under- or overdetermined system of equations AX = B. The effective rank, k, of A, is determined from the QR decomposition with pivoting (see "Algorithm" for details). A solution X is computed which has at most k nonzero components per column. If k < n, this is usually not the same solution as pinv(A)*B, which is the least squares solution with the smallest norm, |X|.

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