Question

syntax question:
for an nxn matrix A, what is ||A|| asking me to find exactly?

Answer 1

Depends on the context! Usually it is either the associated norm of the matrix interpreted as a linear operator or it's simply the determinant.

Answer 2

If A:|R^m->|R^n is a linear operator (a matrix is nothing but a linear operator!), then \[ ||A||:=\sup_{x\not=0} \frac{||Ax||}{||x||} \]
Here ||x|| and ||Ax|| refers to the Euclidean norm in |R^m, |R^n.

Answer 3

the context is this
make vector W a unit vector in the dirction of vector A:
W = A / ||A||

Answer 4

Are you sure A is supposed to be a matrix?

Answer 5

its a vector holding x y z coords.
im using it to do an axis/angle matrix rotation eventually, so it will have to be a vector

Answer 6

So why did you ask about ||A|| if A is a matrix. In your case A is a vector, as you said.

Answer 7

im not sure what to do to compute ||a|| :S

Answer 8

If A=(x,y,z) is a vector, then ||A|| usually refers to the Euclidean norm which is defined as \[||A||:=\sqrt{x^2+y^2+z^2} \]

Answer 9

hm...so when an equation says w = a / ||a||, is it saying that w's x, y, and z are = to a's x / ||a||, a's y / ||a||, and a's z / ||a||?

Answer 10

exactly

Answer 11

oh awesome. thanks a bunch, u totally get a medal