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I need help regarding which topics I should cover to properly learn linear algebra prerequisite for quantum physics. Here's the table of contents:

https://pastebin.com/6EE4NdYA

From what little I know, I'm pretty sure that the chapters: Linear Equations, Vector Spaces, Linear Transformations, Inner Product Spaces and Operators on Inner Product Spaces are necessary. I'd be grateful if someone could tell me about the remaining chapters.

Thanks in advance!