Linear Algebra Example Problems - Coordinate System Representation Example #1

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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 [x]B. We then compute the vector x, the coordinates of [x]B with respect to the standard basis.

  1. Adam Panagos
  2. Coordinate System Representation
  3. linear algebra coordinate vector
  4. linear algebra coordinate mapping
  5. linear algebra coordinates and basis
  6. standard basis representation
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Thank you. So much quicker than Khan academy and you give us the same knowledge.

gavindies
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Wow, I was so confused on this, but now all is clear. Too bad that exam has passed, but this will surely be on the final. Thanks again.

xXBRDNXx
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7 years passed and your videos are still helpful

marioschiras
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Watched so much and read the book. You made it so much easier to understand thank you.

kamron
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I owe you my sanity and ability to sleep tonight

andyhype
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Thank you for this for preparing these videos. This particular video really show what the term ”linear combination” is used for linear transformation.

Belgarathe
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Thank you so much!!! I was struggling for so long lol

garciaoscar
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but I wonder how did you come up with B initially.

wryltxw
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Thank you so much! Very clearly explained

royxss