Linear Algebra Example Problems - Coordinate System Representation Example #2

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When working with vectors we often implicitly use the standard basis. For example, the vector x = [2; -3] tells us the coordinates with respect to the standard basis {[1; 0], [0; 1]}.

At other times it is desirable to work with different coordinate systems that are represented by a different basis. We denote the vector x with respect to the basis B as [x]B.

In this problem we're provided a basis B and the vector x. We then compute the vector [x]B, the coordinates of x with respect to the basis B. We see that the coordinates of x with respect to the basis B can be computed easily by simply constructing and solving a system of linear equations.

  1. Adam Panagos
  2. Coordinate System Representation
  3. standard basis representation
  4. linear algebra coordinate vector
  5. linear algebra coordinates and basis
  6. linear algebra coordinate mapping
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Комментарии
Автор

Thank you Adam. I watched most of the LA videos. It is PERFECTLY done! Excellent!

muhammadalshaghourialhayek
Автор

This is so well explained that it makes me excited to learn more LA. Thank you for such a clear explanation!

syremusic_
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can you show us the process of Reduced Row?

tieeieita
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Is there a way that finds the basis given [x y z] and the coordinates ( a b c )^T?

PortgasDAce
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thanks a lot for your videos particularly the ones about linear algebra. please can you tell me the name of the software you use to make your videos ?

kussila