January 2016 Archives

You're A Complex Fellow, Mr Cholesky

For a complex matrix M, its transpose MT is the matrix formed by swapping its rows with its columns and its conjugate M* is the matrix formed by negating its imaginary part.
A few posts ago I suggested that the conjugate of the transpose, known as the adjoint MH, was sufficiently important to be given the overloaded arithmetic operator ak.adjoint. The reason for this is that many of the useful properties of the transpose of a real matrix are also true of the adjoint of a complex matrix, not least of which is that complex matrices that are equal to their adjoints, known as Hermitian matrices, behave in many ways like symmetric real matrices.
In this post we shall take a look at some of them.

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