Linear Algebra 19e: Illustration of Component Spaces by a Sum of Vectors in ℝⁿ

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  1. MathTheBeautiful
  2. Linear Algebra (Field Of Study)
  3. Matrix Multiplication (Literature Subject)
  4. The Matrix (Award-Winning Work)
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  6. Linear Equation (Literature Subject)
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Prof. Grinfeld, maybe round brackets around the R^n vector would help prevent amateurs (like me) from confusing the vector with its representation. Thank you for these beautiful lectures!

dacianbonta
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+MathTheBeautiful
Suppose 've an image (4 x 4 Pixels). Then if i represent RGB components of each pixel as a column in a matrix, it would be a 3x16 matrix. Now, should i think of each column as vector or components of a vector?? I find it more meaningful to think of it as "components" (RGB) of a vector but then i don't know the basis with respect which these components are obtained. If i treat each column as a vector in R3, the i wouldn't be able to attach any physical significance. It would be consistent with the view presented (i.e to treat each object on its own) though. Could you please help me how should I think to clear my confusion. Thanks.

kumararajaeedara