Question

How to find matrix re of an inner product?

Answer 1

After some more examining of my textbook, I came up with something that might be the answer, though I'd call it sketchy at best. I'd really like to understand this for when finals time rolls around, so if someone could tell me if I'm correct or not (and if not, why) I'd appreciate it very much.

Using equation 6.1.5:

<u⃗ u→, v⃗ v→> = v⃗ TATAu⃗ v→TATAu→

for the purposes of finding ∥w⃗ ∥‖w→‖ the inner product can be represented as<w⃗ ,w⃗ >=w⃗ TATAw⃗ <w→,w→>=w→TATAw→

where w⃗ =(−13)w→=(−13) andA=(1−123)A=(12−13).

∴∥w⃗ ∥=<w⃗ ,w⃗ >−−−−−−−−√=125−−−√=55–√