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## Main Question or Discussion Point

I'm doing an online course in quantum information theory, but it seems to require some knowledge of linear algebra that I don't have.

A definition that popped up today was the definition of the absolute value of a matrix as:

lAl = √(A*A) , where * denotes conjugate transpose.

Now for a given matrix I can calculate the product A*A, but how is the square root of this defined? I have no idea, though I think it should be basis independent, so maybe square root of the trace.

A*A is clearly positive semidefinite but I don't know if I can use that for anything.

A definition that popped up today was the definition of the absolute value of a matrix as:

lAl = √(A*A) , where * denotes conjugate transpose.

Now for a given matrix I can calculate the product A*A, but how is the square root of this defined? I have no idea, though I think it should be basis independent, so maybe square root of the trace.

A*A is clearly positive semidefinite but I don't know if I can use that for anything.