# what are eigen values and eigen vectors

• Feb 28th 2010, 04:38 AM
moonnightingale
what are eigen values and eigen vectors
I read in wikipedia
kindly explain me this.

Instead of writing f(x) we write M(v) where M is a matrix and v is a vector. Kindly explian this with example..
The rules for using a matrix to transform a vector are given in the article linear algebra.
If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix.
• Feb 28th 2010, 07:14 AM
HallsofIvy
Quote:

Originally Posted by moonnightingale
I read in wikipedia
kindly explain me this.

Instead of writing f(x) we write M(v) where M is a matrix and v is a vector. Kindly explian this with example..

I don't see what you are asking. All that is said is that instead of calling the linear transformation "f", they are calling it "M". The second part of that sentence then says that we can always represent a linear transformation as multiplication by a matrix. Do you know what matrix multiplication is?
Presumably, it should be in this link:
Quote:

The rules for using a matrix to transform a vector are given in the article linear algebra.
If the action of a matrix on a (nonzero) vector changes its magnitude but not its direction, then the vector is called an eigenvector of that matrix.
If two vectors have the same direction but possibly different lengths the each is a numerical multiple of the other. If M "changes the magniude but not the direction" of m, then Mv= av where a is a number, then applying the linear transformation to this v is just like multiplying by a number, which is much easier.
Of course, it is true that M0= 0= a0 but if Mv= av for v non-zero, then we say that "a" is an "eigenvalue" of M and v is a corresponding "eigenvector"

It's hard to say more without knowing what you do know and understand about vectors, matrices, linear transformations, and vector spaces.