Singular value decomposition of complex matrix

A system comprising:

• one or more processors;
• one or more computer-readable storage media having thereon computer-executable instructions that are structured such that, when executed by the one or more processors of a computing system, cause the computing system to create a complex matrix singular value decomposition module that performs singular value decomposition of an input complex matrix, wherein the complex matrix singular value decomposition module comprises:
• a correction module configured to correct first singular value decomposition of a real-value matrix representation of an input complex matrix, the first singular value decomposition provided by an intermediate singular value decomposition module, wherein the first singular value decomposition comprises a first left unitary matrix, a first diagonal matrix, and a first right unitary matrix, wherein an upper left half of the diagonal of the first diagonal matrix is not identical to the lower right half of the diagonal of the first diagonal matrix,
• wherein the correction module is configured to perform the correction to formulate a second singular value decomposition of the real-value matrix representation of the input complex matrix by performing:
• an act of formulating a second diagonal matrix, such that the diagonal of the second diagonal matrix represents the value of the diagonal of the first diagonal matrix, but shuffled so that the upper left half of the diagonal of the second diagonal matrix is the same as the lower right half of the diagonal of the second diagonal matrix.

A computer-implemented method for performing singular value decomposition of an input complex matrix, the method comprising:

• an act of converting the input complex matrix into a real-value matrix representation of the input complex matrix;
• an act of providing the real-value matrix representation to an intermediate singular value decomposition module to perform singular value decomposition of the real-value matrix;
• an act of accessing a first singular value decomposition of the real-value matrix representation from the intermediate singular value decomposition module as a result of performing singular value decomposition of the real-value matrix, the first singular value decomposition comprising a first left unitary matrix, a first diagonal matrix, and a first right unitary matrix, and an upper left half of the diagonal of the first diagonal matrix not being identical to the lower right half of the diagonal of the first diagonal matrix, and
• an act of correcting the first singular value decomposition to create a corrected second singular value decomposition by performing:
• an act of formulating a second diagonal matrix, such that the diagonal of the second diagonal matrix represents the value of the diagonal of the first diagonal matrix, but shuffled so that the upper left half of the diagonal of the second diagonal matrix is the same as the lower right half of the diagonal of the second diagonal matrix;
• an act of formulating a second left unitary matrix based on the first left unitary matrix and correlated with which of the values of the diagonal of the first diagonal matrix were shuffled to formulate the diagonal of the second diagonal matrix;
• and
• an act of formulating a second right unitary matrix based on the first right unitary matrix and correlated with which of the values of the diagonal of the first diagonal matrix were shuffled to formulate the diagonal of the second diagonal matrix.