[分析] n次齊次多項式的維度

[a88241050 (難道阿宅錯了嗎)]

設X1, X2, ..., Xn之多項式U(X1, X2, ..., Xn)滿足


(1) U(t X1,t X2,...,t Xn)= t^k U(X1, X2, ..., Xn), k為已知正整數


(2) U11+U22+...+Unn = 0  (二階偏導函數總和=0, 即Laplace eq.)


這些函數U(X1, X2, ..., Xn)形成一個vector space V over R


試求 dim(V)  (以 n, k表示)



--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 140.135.32.98
→ cgkm        :未證先猜 dim(V) = max{n-k, 0}