那個▽是gradient，是多變數函數的方向導數，類似單變數函數的微分 例 f(x,y)=x^2+3xy+2y^2+4x+5y+6 grad(f(x,y))=(2x+3y+4,3x+4y+5) 至於|| ||則是 norm ，意思跟向量長度類似
... suppose that the topology of C[0,1] is given by the sup norm , since you have not stated it. Since D is dense in...
||˙|| 在數學上稱為 範數 ( norm ), 故 || X-Y|| 稱為 X-Y 的 範數. 範數 在所屬空間的定義有所不同, 如 長度 就是其中一種, 當然, 還有 有限能量範數 等等... 以上敬請參考 !
We can treat R as a normed vector space with the absolute value norm over the field Q. The norm topology of this vector space is clearly...
...;= ||A|| ||B||, where ||x|| denotes the length or the norm of the vector x. Carefully pick vectors as A=(y, (1-y^2...
... in S. Let M>0 be the max. L^2 norm of grad(f) on S. For ε>0, takeing δ= min(δ1, &epsilon...
...顯然 y_m ∈ X〔因為有限項非零！〕, 且 y_m → y (in ℓ^1- norm )。 所以，X 在 Y 內是稠密的。 因此 X 不為 Y 之...
...functional is evident. To show boundedness, take any g in L2(λ) with norm not greater than 1. Then |F(g)| = |∫ g dμ| ≤ &int...
