If A is a symmetric matrix, then verify that A×A' (transpose) and also A'×A is also symmetric
Asked
Active
Viewed 1,639 times
-1
-
I'm looking for where to start – Pp Broski Sep 01 '19 at 15:31
-
1Already answered here – Manoj Kumar Sep 01 '19 at 15:33
-
Begin by proving : $$(1);;(A^t)^t=A;,;;;(2);;(AB)^t=B^tA^t$$ The above is all you need now. – DonAntonio Sep 01 '19 at 15:40
-
The claim holds for every $m\times n$ matrix. – amsmath Sep 01 '19 at 15:52
1 Answers
0
Note that in general $$(AB)'=B'A'$$
For a symmetric matrix we have $A'=A$
$$AA'=A'A=A^2$$ $$(AA')'=A''A=A^2=AA'$$ $$(A'A)'=A'A''=A^2=A'A$$
Mohammad Riazi-Kermani
- 68,728