i******n
发帖数: 839 | 1 A and B are idempotent, prove AB is idempotent as well, provided A and B
commute in multiplication.
Help please,
I thought A and B should also be symmetric for AB to be Idempotent. |
A*******s
发帖数: 3942 | 2 i forget most of what i learned in linear theory, but i do remember
sometimes the matrices are assumed to be symmetric in the context about
quadratic forms.
【在 i******n 的大作中提到】
: A and B are idempotent, prove AB is idempotent as well, provided A and B
: commute in multiplication.
: Help please,
: I thought A and B should also be symmetric for AB to be Idempotent.
|
y*****t
发帖数: 1367 | 3 这。。这不是很简单吗？直接把乘积写出来就证明了～
【在 i******n 的大作中提到】
: A and B are idempotent, prove AB is idempotent as well, provided A and B
: commute in multiplication.
: Help please,
: I thought A and B should also be symmetric for AB to be Idempotent.
|
l*********s
发帖数: 5409 | 4 AB=BA --> (AB)(AB)=A(BA)A=A(AB)B=(AA)(BB)=AB |
p**********l
发帖数: 1160 | 5 I forgot a lot too.
But I think there is a typo here.
【在 l*********s 的大作中提到】
: AB=BA --> (AB)(AB)=A(BA)A=A(AB)B=(AA)(BB)=AB
|
l*********s
发帖数: 5409 | 6 Thanks for pointing out ^__^
【在 p**********l 的大作中提到】
: I forgot a lot too.
: But I think there is a typo here.
|
p**********l
发帖数: 1160 | 7 We all make this type of mistakes from time to time, hehe.
【在 l*********s 的大作中提到】
: Thanks for pointing out ^__^
|
i******n
发帖数: 839 | 8 man, "A and B commute in multiplication" means "AB=BA".
I thought it only means, the product of AB exists.
Then it is a relief.
thanks.
English, always my pain.
【在 l*********s 的大作中提到】
: AB=BA --> (AB)(AB)=A(BA)A=A(AB)B=(AA)(BB)=AB
|
