Matrix representation of complex space

quasar_4
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more on the complexification of a vector space.

if we complexify some space V, then how does the matrix representation of some linear T on V relate to the matrix representation of T on Vc on the standard ordered basis for V?
 
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same matrix.
 
oh, okay, I think I am seeing it. I think I need more coffee. :P
 

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Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

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Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
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