MHB Linear Algebra Expert Requested For Discussion

bwpbruce
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I was wondering if there was anyone comfortable enough about basic to advanced linear algebra concepts who would be willing to participate in a chat/whiteboard based platform to discuss or answer questions concerning such concepts. I need clarification on a few things
 
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Hi bwpbruce,

What topics specifically do you need help with?
 
Euge said:
Hi bwpbruce,

What topics specifically do you need help with?

Just some questions about Linear Equations, Linear Combinations, and the Zero Vector. I prefer if we discuss it in chat. This forum setup isn't ideal for me.
 
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The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
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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