Conjugate transpose: Difference between revisions

Revision as of 22:26, 8 September 2020

Revision as of 15:27, 12 September 2020

Line 58:

That is, denoting each ''complex'' number ''z'' by the ''real'' 2&times;2 matrix of the linear transformation on the [[Argand diagram]] (viewed as the ''real'' vector space <math>\mathbb{R}^2</math>), affected by complex ''z''-multiplication on <math>\mathbb{C}</math>.

THusThus, an ''m''-by-''n'' matrix of complex numbers could be well represented by a 2''m''-by-2''n'' matrix of real numbers. The conjugate transpose therefore arises very naturally as the result of simply transposing such a matrix—when viewed back again as ''n''-by-''m'' matrix made up of complex numbers.

==Properties of the conjugate transpose==