What will i use in Quantum maths from linear algebra?


by Ayham
Tags: algebra, linear, maths, quantum
Ayham
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#1
Jan29-13, 10:47 AM
P: 16
What is the linear algebra background for Quantum maths? Matrices? Basis's? Matrix trans.? Coordinate Systems?
Please help me, and im sorry if i posted this in the wrong place...
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mfb
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#2
Jan29-13, 12:19 PM
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Quote Quote by Ayham View Post
Matrices? Basis's? Matrix trans.? Coordinate Systems?
All of them are relevant.
Plus some general properties of vector spaces, different bases, eigenvalues of various operators and so on.
Fredrik
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#3
Jan29-13, 04:31 PM
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Complex vector spaces, linear independence, bases, inner products, inner product spaces, orthonormal bases, linear operators, matrices, matrix multiplication, a theorem about which matrices are invertible, the relationship between linear operators and matrices, the adjoint operation, self-adjoint linear operators, eigenvectors and eigenvalues, and the spectral theorem.

Since the relationship between linear operators and matrices is very important, I recommend that you use a book that presents those things early in the book, like Axler or Friedberg, Insel & Spence. (I have only read the former, but I've heard good things about the latter).

You may not need all of those things for an introductory course. It may be enough to understand complex inner product spaces, orthonormal bases and self-adjoint linear operators. But you will need the rest if you want to get good at QM.


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