#grouptheory #linearalgebra #matrices #representationtheory #complexnumbers
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How can the complex numbers be represented as matrices? This is an excellent warm-up for more general matrix representations later. We look at complex conjugates, the trivial representation, the determinant, and much more.
Many thanks to professor Karel Dekimpe from the university of Leuven for helping me understand representations and characters.
0:00 Integer powers of i
3:52 Rational powers of i
6:47 Real powers of i
8:41 The entire complex plane
10:48 How the real numbers are represented
11:32 Reflections & complex conjugation
13:38 Degrees of freedom
17:48 The trivial representation
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( https://creativecommons.org/licenses/by/4.0/ )