09/29 - Analogy to Vector Spaces: Difference between revisions
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**<math> \hat v_1, \hat v_2, \hat v_3 </math> are the basis vectors |
**<math> \hat v_1, \hat v_2, \hat v_3 </math> are the basis vectors |
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**A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of <math>\real^n</math> |
**A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of <math>\real^n</math> |
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The dot (scalar) product takes two vectors over the real numbers and returns a real-valued scalar quantity. Geometrically, it will show the projection of one vector onto another. |
Revision as of 12:46, 6 November 2008
Let the vector be defined as:
-
- are the coefficients
- are the basis vectors
- A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of
The dot (scalar) product takes two vectors over the real numbers and returns a real-valued scalar quantity. Geometrically, it will show the projection of one vector onto another.