Show that the product of two upper triangular matrices is upper triangular matrix

• January 18th 2011, 07:51 PM
Jskid
Show that the product of two upper triangular matrices is upper triangular matrix
Show that the product of two upper triangular matrices is upper triangular matrix.

I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

My question is how do you actually write this?
• January 18th 2011, 07:59 PM
FernandoRevilla
Hint :

If $A=(a_{ij})$ and $B=(b_{ij})$ are $n\times n$ matrices, and $AB=(c_{ij})$ use:

$c_{ij}=\displaystyle\sum_{k=1}^n{a_{ik}}b_{kj}$

Fernando Revilla
• January 18th 2011, 08:24 PM
Drexel28
Quote:

Originally Posted by Jskid
Show that the product of two upper triangular matrices is upper triangular matrix.

I know this is true because in the lower part each term will be multiplied by 0 (so in the lower part each element will be 0(a)+0(b)...+0(z))

My question is how do you actually write this?

And the characterization of "the lower half is zero" in terms of these $a_{i,j}$s' Dr. Revilla speaks of.