Eigen Values and Eigen Vectors

When we look at the eigen vectors of a matrix , it actually gives us a vector that doesnt change the direction when the matrix is applied … (Ofcourse it is allowed to rotate 180 degrees ….) . At the same time the vector is shrunk to an extent .

If B is the matrix and v is the  eigen vector with an eigen value k.

B * v = k*v

if k < 0 then its rotated by 180 degrees.  the Eigen vector is shrunk by k.

If B is a symetric matrix then it has linearly independent eigen vectors.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: