What is the Gist of the “Conjugate Transpose” (of a Matrix)?

“In mathematics, the conjugate transpose or Hermitian transpose of an m-by-n matrix  with complex entries is the n-by-m matrix  obtained from  by taking the transpose [of A] and then taking the complex conjugate of each entry [in that transpose]. (The complex conjugate of , where  and  are real numbers, is .)” (“Conjugate transpose,” Wikipedia, retrieved 6/9/2020)

“The reason we want to do this [as opposed to just taking the conjugate] is so that we can multiply the matrix and the conjugate transpose. Simply taking the conjugate will not give us matrices we can multiply if they are not square.” (“Complex, Hermitian, and Unitary Matrices,” Professor Dave Explains)

In addition, it seems like the conjugate transpose is fundamental in defining several other matrices (as talked about here) and has several useful properties (such as these)

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Disclaimer:

I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).