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# 在Matrix Algebra的Impossible難題!!

如果A=[1 -1 0]

. 0 1 1

題目A^2=Impossible

那(A^T)A呢?

T的意思是不是行數變列數,列數變行數,即[1 0]

. -1 1

. 0 1

請解我心中難題

1)T的意思我上面對不對?

2)(A^T)A答案是Impossible? 還是 [-1 -1 0]

. -1 2 1

. 0 1 1

如果A=

[1 -1 0]

0 1 1

題目A^2=Impossible

那(A^T)A呢?

T的意思是不是行數變列數,列數變行數,即

[1 0]

-1 1

0 1

請解我心中難題

1)T的意思我上面對不對?

2)(A^T)A答案是Impossible? 還是

[-1 -1 0]

-1 2 1

0 1 1

為什1麼A^2=Impossible呀?

是固定的道理嗎?

### 2 Answers

- JacobLv 61 decade agoFavorite Answer
If A is mxn, B is nxp, then AB is mxp.

Now A is 2x3, thus A^2 is undefined.

However, A^T is 3x2, thus (A^T)A is 3x3, which is well-defined.

In your case, your T concept is correct,

but (A^T)A is wrong, the (1,1) entry should be 1 instead of -1.

A^n only exist when A is a square matrix.