Orthogonal bases are easy to work with!

Description: We can extend the idea of two orthogonal vectors to an orthogonal set of vectors. Then, if you have an orthogonal basis opposed to a normal basis, trying to expand a vector in the basis is a much easier task; each coefficient is determined by a couple dot products only.

Learning Objective:
1) Verify that a set is an orthogonal set
2) Given an orthogonal basis and a vector, expand the vector in terms of that basis without using row reductions.

This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati

[SS-plci]

What is that V symbol that looks like an upward angle on the right at 0:01 mean...?

[larshaji]

you have a great channel but you are missing playlists for your videos

[hyperduality]

Perpendicularity, orthogonality = DUALITY!
The inner product is dual to the cross product -- Maxwell's equations for photons or pure energy is dual.
Electro is dual to magnetic, positive is dual to negative, north poles are dual to south poles.
Independence is dual to dependence.
"Always two there are" -- Yoda.