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

1. 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?

2. 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

3. 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.