Re: [理工] 線代 TorF

看板Grad-ProbAsk作者KAINTS (RUKAWA)時間13年前 (2013/01/31 00:42)推噓7(7推 0噓 16→)

留言23則, 6人參與討論串3/3 (看更多)

※ 引述《zero200488 (Kiowa)》之銘言： : 1.A linear transformation is onto if and only if the column of its standard : matrix span its range.-------------------F 改成the row of its standard matrix 用到的觀念是假設T:V ->W ;dim(V)=n,dim(W)=m,B為V中ㄧ組有序基底，存在[T]B=A,A is m by n onto -- rank(T)=dim(W)=m,可得A為列獨立 : 2.The ptoduct of square matrices is always defined.---------------F 矩陣相乘必須滿足前者行數等於後者列數 : 3.The pivot columns of the reduced row echelon form of A form a basis for : the column space of A.-------------F rref做的運算是列運算，不改變其列空間，其pivot rows則為該列空間之基底，若要為該行空間之基底，必須為square : 4.Every square matrix has a complex eigenvalue.----------T : 為什麼? real contain in complex,so it is alwyas ture. : 5.Let W be a two-dimensional subspace of R^3. The orthogonal projection : operator onto W is onto.---------------F 這題感覺前面這句話"two dimensional subspace of R^3",就錯了，二為空間怎麼可能會是三維的子空間 ex,W=span{(0,1),(1,0)}怎麼展延都不會是R^3 : 6.For a given set of data plotted in the xy-plane,the least-squares line is : the unique line in the plane that minimizes the sum of the vertical distan- : ces from the data points to the line.---------F "unique" 要行獨立才會唯一 : 問題有點多謝謝以上有誤煩請指教 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 123.193.7.20 ※ 編輯: KAINTS 來自: 123.193.7.20 (01/31 00:48)

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