The Standard Inner Product on R^n

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1. For some reason this is consistently what I find most confusing about linear algebra. I'm naturally pretty good at plain geometry too, and can visualize 3 dimensions no prob. The issue is that I don't think in equations or in a procedural, algebraic way. I end up just knowing the solution without knowing how to write down my steps in the language of algebraic equations. And furthermore, procedural manipulations of equations never helps me understand anything -- in anything it makes less clear what I already knew before seeing the equations.
   
   I honestly believe I could make up my own language that would be more effective for me than algebra.
   
   With this said, I've been forcing myself to learn the accepted notation and am masking progress. Your videos help me out a lot.
2. Thanks so much for making this video!  The way you explain things makes a whole lot more sense than my textbook!  One question I had -- at around 2:25 you say to throw away the 2.  Can you explain why you're able to do this?  Thanks again!
3. Towards the end of the video, where you have -6<e1,e1>+2<e1,e2>+(-9<e2,e1>+6<e2,e2>), should it not be +4<e1,e2>, instead of 2<e1,e2>? By the way, thank you so much for your help!
4. Your videos about linear algebra helped me a lot. Thank you!
5. Your welcome! I'm at CUNY(Medgar Evers) this semester.
6. Thanks so much! I wish you taught at my college.
7. Thank you MathDoctorBob!
8. Your welcome, and good luck with exams! Not only that, but you can watch it when convenient, which I find great for my students with jobs and families.
9. Thank you so much for this! Extremly appreciated!
10. It comes from the law of cosines, which requires some pictures (as in the vid). To remember, we get zero when the vectors are perpendicular, which also occurs as in cos(90). We use sin(theta) in the cross product, which is closely related to the inner/dot product.
11. I dont understand why an inner product contains that cos (theta), why not sin(theta)?
12. You're welcome! 
13. Great video, this really cleared things up I wasn't sure what my instruction was talking about
14. Thanks! Glad to be of help.
15. Any specific problems? I can shoot them quickly. - Bob
16. If you have any specific problems you need, send them. I can shoot example videos much faster than general theory. - Bob
17. now
18. Definitely. I'll put it in the queue. You may want to look at what follows in the playlist (Example of Fourier's Trick especially). There's enough for orthonormality, but I haven't done a formal video on projections. - Bob
19. videos on orthonormality & projection operators please?
20. @thebigbangtheoryftw Glad to be of help! I'm planning on filling the gap from here to the Gram-Schmidt process. - Bob