09/29 - Analogy to Vector Spaces: Difference between revisions

Revision as of 12:20, 6 November 2008

Let the vector ${\vec {v}}$ be defined as:

${\vec {v}}=a_{1}\cdot {\hat {v}}_{1}+a_{2}\cdot {\hat {v}}_{2}+a_{3}\cdot {\hat {v}}_{3}$ ${\vec {v}}=a_{1}\cdot {\hat {v}}_{1}+a_{2}\cdot {\hat {v}}_{2}+a_{3}\cdot {\hat {v}}_{3}$
- $a_{1},a_{2},a_{3}\,\!$ are the coefficients
- ${\hat {v}}_{1},{\hat {v}}_{2},{\hat {v}}_{3}$ are the basis vectors
- A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of $\Re ^{n}$

@@ Line 1: / Line 1: @@
-Let the vector '''v''' be defined as:
+Let the vector <math> \vec v </math> be defined as:
 *<math>\vec v = a_1 \cdot \hat v_1 + a_2 \cdot \hat v_2 + a_3 \cdot \hat v_3</math>
+**<math> a_1, a_2, a_3 \,\!</math> are the coefficients
+**<math> \hat v_1, \hat v_2, \hat v_3 </math> are the basis vectors
+**A vector basis is a set of n linearly independent vectors capable of generating? an n-dimensional subspace? of <math>\real^n</math>