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To be used for linear algebra, and closely related disciplines such as tensor algebras and maybe clifford algebras.

6 votes
3 answers
450 views

Why does it matter that a passive transformation can be "interpreted" as an active transform...

In most mathematics textbooks I have read (see e.g. Axler), the change of basis (COB) matrix has been introduced as a useful computational tool for expressing components of vectors in different bases. …
EE18's user avatar
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1 vote
1 answer
131 views

Commuting normal operators have common eigenbasis?

One often finds in quantum mechanics textbooks (for physicists) a "proof" that self-adjoint and commuting operators $A,B$ have a common eigenbasis. However, in the standard proof of Bloch's theorem (s …
EE18's user avatar
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4 votes
2 answers
862 views

Why this definition of the trace?

It is common in quantum mechanics textbooks (e.g. Ballentine page 15) to define the trace of an operator as the sum of its diagonal elements in an orthonormal basis in particular. Why is this definiti …
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