Definition questions for linear algebra

[futeca]

i am having trouble understanding some of the "basic" concepts of my linear algebra...any help would be greatly appreciated

what is an orthogonal basis? and how to construct it? i keep stumbling upon questions asking about construction a orthogonal basis for {v1, v2} in W

what i null A? need to understand the concept fro proofs

what is Col A? also need to understand for proofs

what exactly is a projection? i know the formula for it and i know how to apply it yet i don't understand the concept of what it is or how to picture it

thank you

 

[DonAntonio]

i am having trouble understanding some of the "basic" concepts of my linear algebra...any help would be greatly appreciated

what is an orthogonal basis? and how to construct it? i keep stumbling upon questions asking about construction a orthogonal basis for {v1, v2} in W

what i null A? need to understand the concept fro proofs

what is Col A? also need to understand for proofs

what exactly is a projection? i know the formula for it and i know how to apply it yet i don't understand the concept of what it is or how to picture it

thank you

Best advice ever: get yourself a good linear algebra book...:)

Ort. basis: read about Gram-Schmidt process and def. of orth. basis

Null A = most probably it means the null (sub)space of a matrix (or linear transformation) A, and it is the set of all vectors that A maps to the zero vector

Col A = probably it means the space spanned by the columns of an n x m matrix in the vector space $\mathbb F^n$

DonAntonio

 

[futeca]

thank you so much this is great help!

btw do u happen to have any recommendations for a good linear algebra book to buy?

 

[Sankaku]

No need to buy. Here is a good one for free:

http://joshua.smcvt.edu/linearalgebra/

Here are some easier notes if that is too fast for you:

http://tutorial.math.lamar.edu/