What is the Norm of a Vector and How is it Used in Linear Algebra?

[LeakyFrog]

Hello, I am studying for an exam in Linear Algebra. My teacher gave us an outline of things that we need to know and one of them is this:

Find the norm of a vector v in n-dimensional space. Use it to find a unit vector in the same direction as v.

I was just hoping someone might be able to explain what exactly that means. I understand what a unit vector is but I'm a little hazy on the rest. Such as what exactly is a normal vector to another vector? Is that simply a vector that is perpendicular to the other? Any help would be awesome.

 

[Sethric]

Not normal, norm. They are two different things. In n-dimensional space, the most common norm is the square root of the inner product, or dot product. It gives a concept of length to a vector. How would you use a vector's length to find a unit vector in the same direction?

 

[LeakyFrog]

Dude thank you soooo much for clearing that up. Makes perfect sense now. And I learned what norm means. F' Yeah!

 

[HallsofIvy]

I was kind of worried! Reviewing for a test in linear algebra and did not know what the "norm" of vector was? But I can see confusing "norm" and "normal".