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Suppose that $A$ and $B$ are $n$ dimensional, upper triangular matrices. How many floating point multiplications are necessary to compute $AB$?

Typically a $$ nxn $$ matrix requires $$ n^2 $$ multiplications with a vector. Thus multiplying 2 $$ nxn $$ matrices would require $$ 2n^2 $$ multiplications and $$ 2n (n-1) $$ operations to sum the products.

## Comments

Typically a $$ nxn $$ matrix requires $$ n^2 $$ multiplications with a vector. Thus multiplying 2 $$ nxn $$ matrices would require $$ 2n^2 $$ multiplications and $$ 2n (n-1) $$ operations to sum the products.