Advanced Linear Algebra - Lecture 17: What is an Inner Product?

We learn about inner products as generalizations of the dot product. We also introduce the standard inner product on a few vector spaces, and one weird non-standard one.

Please leave a comment below if you have any questions, comments, or corrections.

[michaelfrench]

Oh my god, thank you so much for clearly explaining why the conjugates are used!!!!

[quantabot]

Ah finally a video with comments..I reached 18th video. Im enjoying this, it just keeps getting better,

[rogeriliffe]

In every single other math book that I have found the inner product for complex numbers is linear in the first entry and the second vector is conjugated. This is the case for the Wikipedia entry for inner product, in Luenberger's book on Optimization, in Sheldon Axler's book "Linear Algebra Done Right" and in Byth and Robertson's book "Further Linear Algebra". Is this a quantum mechanics quirk? I cannot get the standard Gram-Schmidt formula to work on complex numbers when I use your method.

[palantea]

An inner product is such that it's linear in some argument, doesnt matter which one is? and why would it be

[michaelli]

In part (c) of the last example, where do v1 and v2 come from? Should they both be just v?