Proving a matrix is always symmetric

Question

$B$ is a square matrix of real numbers. Show that the matrix $BB^T$ is always symmetric.

Note that $(AB)^T = B^TA^T$ – Ben Grossmann Sep 21 '14 at 23:35 — Ben Grossmann, Sep 21 '14 at 23:35

score 2 · Answer 1 · answered Sep 21 '14 at 23:36

2

$(B\cdot B^{t})^{t} = (B^{t})^{t}\cdot B^{t}= B\cdot B^{t}$

answered Sep 21 '14 at 23:36

TheOscillator

Are you able to justify/prove how you got this in words? – Irwin Sep 21 '14 at 23:37
We say that a square matrix A is symmetric if $A^{t}=A$ where $A^{t}$ denotes the transpose of A. You should look up the definitions more carefully. – TheOscillator Sep 21 '14 at 23:41

score 0 · Answer 2 · answered Sep 21 '14 at 23:34

0

$$(BB^t)^t=(B^t)^tB^t........$$

answered Sep 21 '14 at 23:34

Timbuc

Are you able to justify/prove how you got this in words? – Irwin Sep 21 '14 at 23:36
It follows from the definitions: $;(AB)^t=B^tA^t;$ for any two square matrices. Do it. – Timbuc Sep 21 '14 at 23:37

2 Answers2