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4 votes
1 answer
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Can someone explain why we define adjoint?

Recently I've been reviewing linear algebra. The definition of adjoint of a linear map on an inner product space seems not really natrual. Looks like people use this to define normal and self-adjoint ...
jiefu hou's user avatar
-1 votes
2 answers
649 views

Matrix representation of adjoint & co-adjoint orbit of $so(3)$

So I am trying to find the co-adjoint orbits of the lie algebra $so(3)^*$ from this example but I am stuck with a very trivial linear algebra property now I found the adjoint orbits and I know the ...
Sasha's user avatar
  • 697
1 vote
0 answers
257 views

Any connection between the adjoint map that has determinant $det(\phi)^{(n-1)}$, and the adjoint map that has determinant $ det\phi$?

Is there any connection between the adjoint mapping that is introduced while studying the matrices, and the adjoint mapping that is introduced while studying inner product spaces ? I mean, for ...
Our's user avatar
  • 7,377