Linear algebra Upper Triangular matrix

Question

I have a question regarding upper triangular matrix.

I know that if AB is upper triangular then the |AB| equals to the diagnoal multiplication, but It doesn't seem to help me here.

If AB is upper triangular and non-singular then A and B both upper triangular?

Notice that A and B are both square.

I can't choose AB = 0 becuase its signular....

Yes they are both square matrices – SyndicatorBBB Oct 29 '12 at 08:36 — SyndicatorBBB, Oct 29 '12 at 08:36
Never mind, didn't read the question properly... – wj32 Oct 29 '12 at 08:37 — wj32, Oct 29 '12 at 08:37

score 1 · Answer 1 · answered Oct 29 '12 at 08:40

1

No, $A$ and $B$ does not necessarily have to be upper triangle. For example, $$\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$$

answered Oct 29 '12 at 08:40

EuYu

42,984

Wow so simple......... Thank you very much! – SyndicatorBBB Oct 29 '12 at 08:43
I have one more question to ask but I don't want to open mass of questions. can I assign it here? – SyndicatorBBB Oct 29 '12 at 08:44
@Guy: What is it? – wj32 Oct 29 '12 at 08:47
I was wondering about one adjugate matrix property.
I know that If $A$ is symmetric so is $adj(A)$.

I was thinking to myself, is the opposite direction is also TRUE?

If $adj(A)$ is symmetric then $A$ is symmetric ?

Thank you.
– SyndicatorBBB Oct 29 '12 at 08:49
@wj32 see above. about the adjugate matrix. – SyndicatorBBB Oct 29 '12 at 08:49
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@Guy: Take a $3 \times 3$ matrix with a 1 in the upper-right corner (or anywhere). – wj32 Oct 29 '12 at 08:54
damn missed you answer till now. Thank you very much ! – SyndicatorBBB Oct 29 '12 at 09:52

Linear algebra Upper Triangular matrix

1 Answers1