推 jacky7987 :rank(A)是符號 前面的RANK是英文 12/30 02:09
→ jacky7987 :(a)就照著定義數 12/30 02:10
→ jacky7987 :invertible就行完全獨獨立 12/30 02:10
→ jacky7987 :2.(a) 想一下A^T 和[1,...,1]這個向量 12/30 02:10
1.The RANK rank(A) of a matrix A is the maximum number of linearly independent
rows in A. (大寫的rank在原題目敘述中是斜體字,不知道為什麼要兩個rank)
(a) Prove that for any m*n matrix A and any n*p matrix B, we have
rank(AB)<=rank(B).
(b) Prove that for any n*n matrix A and any n*p matrix B, if A is invertible
then rank(AB)=rank(B).
2.Suppose M is an n*n matrix in which all entries are nonnegative and all
column sums are 1.
(a) Prove that 1 is an eigenvalue of M
(b) Prove that for each eigenvalue λ of M, we have |λ|<=1.
這兩題想很久都想不太出來...
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