Linear Algebra - Lecture 31 - Coordinate Systems

In this video, I review the definition of basis, and discuss the notion of coordinates of a vector relative to that basis.

The properties of a basis of a subspace guarantee that a vector in that subspace can be written as a linear combination of the basis vectors in only one way. The weights in that unique linear combination are called the coordinates of the vector relative to that basis.

[adnanhowlader]

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[soram]

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[micah]

Paused at 6:13…
I suspect that coordinates are like the inverse function of a translation.

So let A equal the vectors v1 and v2, where the basis is {v1, v2}and let vector y be the solution for the translation of T(x)=Ax, then if you plug in the coordinates of vector y relative to the basis into x for T(x) = Ax you get vector y as a result.

[studywithme]

In the previous example ( example 2 @7:21)you have never assumed that B spans H. Why is it @10:39 you simply assume it spans H?