Null Vectors vs. Degenerate Vectors

Symmetric bilinear forms are generalizations of inner products that allow for vectors to square to any scalar value, not just positive numbers. This leads to some new kinds of vectors: null vectors and degenerate vectors. While many people think they are the same, it is possible for a null vector to not be degenerate.

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[evandrofilipe]

You really hit the nail on the head there, i thought they were the same

[khiemgom]

Plz make sure the content is in the middle and esp not below so not to get hidden behind the title

[deronlessure]

This was quite helpful, thank you. But (I believe) inner products are only bilinear over R. Over C they are linear in the first component and conjugate linear in the second (note: physicsts have it reversed)

[Pedritox]

Be careful with which vector you have around, a dot product could convert you in a degenerate vector

[jacksonstenger]

Excuse my ignorance, but would you give me an example of a vector v such that v^2 = -1? Perhaps it relates to imaginary numbers in some way. Everything else in the video makes perfect sense to me, it would just be nice to see a concrete example where v^2 = -1.

[APaleDot]

I'm confused why the (e_1)(e_2) term is 0. Are you only working with dot product here?

[linuxp]

Are dual numbers, symmetric bilinear forms?