Working with Matrices and Vectors
In quantum mechanics, we frequently multiply matrices as well as matrices with vectors. As shown in "Fundamental Theorem of Linear Algebra" [Str93], although the mechanics of these types of multiplications may seem arbitrary, they offer a point of view that gives us a way to represent the operation of gates on quantum states. (For a lucid description of linear algebra in a practical setting, especially the discussion relating to the columns of a matrix, which is of the most interest to us, see Foundations of Network Optimization and Games [FB16].)
A matrix is an array of numbers arranged as follows:
In this ...
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