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Will this work for complex matrix. If the matrix is rank deficient will this give a psuedo inverse. which inversion method is computationwise most effective. I wanted to implement complex matix inversion in a DSP processor.
First this works for complex matrix.
second I didn't undersatnd you second sentence "If the matrix is rank deficient will this give a psuedo inverse".
Third there are a lot of inversion matrix methodes and every one has a domain of applicability I can not say that there someone which more efficient in general than the others. But I think it depends on the matrix kind and size!
For inversing a matrix in order to solve a linear system, a lot of methods exist.
Obviously, the use of a method rather than another depends on dimension and nature of the same matrix.
Which kind of matrix are you considering? I mean, is it a sparse matrix? Is an Hermitian one? what about elements? ..are they complex or not? Is the matrix a square one? what is its dimension?