Signatures of Hermitian Forms and Unitary Representations Talks Www Math Mit

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Professor Dave here, let’s look at complex matrices. Up until now, we’ve been focusing a lot on real matrices, that is, matrices where all of the entries are real numbers. Now it’s time to consider complex matrices, which are matrices in which some of the entries contain complex numbers. If you need a little review regarding comlex numbers, what they are and relevant operations, check out this tutorial from earlier in the series. Otherwise, let’s dive right in. We can simply recall that complex numbers are numbers with a real part, a, and an imaginary part, bi, where i is the square root of -1, and as we said, we can find complex numbers in matrices. Just the way we can separate complex numbers into a real component and an imaginary component, we can separate matrices into a real matrix A and an imaginary matrix iB. For example, let’s consider the 2 by 3 matrix 2 + 3i, i, 6 - 4i; 7, 2 - 3i, -i. We can split this complex matrix up into a real part plus an imaginary part by kee