2/4/15
... in V ⊗ W can be written in this form. For example, if dim V, dim W ≥ 2 and {v1 , v2 } and {w1 , w2 } are linearly independent in V and W , respectively, then v 1 ⊗ w1 + v 2 ⊗ w2 is not a pure tensor. Example 0.1. If W = F then V ⊗ W ∼ =V. Example 0.2. Let V = W = F , and let µ : F × F → F be the usu ...
... in V ⊗ W can be written in this form. For example, if dim V, dim W ≥ 2 and {v1 , v2 } and {w1 , w2 } are linearly independent in V and W , respectively, then v 1 ⊗ w1 + v 2 ⊗ w2 is not a pure tensor. Example 0.1. If W = F then V ⊗ W ∼ =V. Example 0.2. Let V = W = F , and let µ : F × F → F be the usu ...
intuition
... • There exists a function f(t) (called scaling function) such that f (t k ) : k integer is a basis for V0 • If f (t ) Vk then f (2t ) Vk 1 and vice versa • lim V j L2 ( R) ; V j {0} j ...
... • There exists a function f(t) (called scaling function) such that f (t k ) : k integer is a basis for V0 • If f (t ) Vk then f (2t ) Vk 1 and vice versa • lim V j L2 ( R) ; V j {0} j ...