Why does the transpose operator take the complex conjugate?
When performing linear algebra operations on complex matrices, it is almost always the complex conjugate transpose (also called the Hermitian transpose) that is needed (see Gilbert Strang’s linear algebra book for discussion- page 293 in edition 3). The bare apostrophe is an operator that takes the complex conjugate transpose. The non-conjugating transpose operator is a period followed by an apostrophe. Type help punct for more info.