[線代] similar的觀念
let A and B be n*n matrices
show that if A is similar to B, then there exist n*n matrices S and T,
with S nonsingular, such that
A=ST and B=TS
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我這樣證
已知A is similar to B, 所以存在nonsingular P使得 A = P^(-1)BP
因P為nonsingular, 所以P^(-1)亦為nonsingular
令S為P^(-1), T為BP, 即A=ST, 得證
A=P^(-1)BP, PAP^(-1)=B, 令S為P^(-1), T為BA, 即B=TS, 得證
可是這樣T就不一樣了，這樣證可以嗎?
如果不行 應該怎麼證比較好呢?
謝謝
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