- #1

orochimaru

i have trouble understanding these two terms.

can anyone explain to me eigenvalues and eigenvectors in laymen terms?

Thks in advance!

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter orochimaru
- Start date

- #1

orochimaru

i have trouble understanding these two terms.

can anyone explain to me eigenvalues and eigenvectors in laymen terms?

Thks in advance!

- #2

Galileo

Science Advisor

Homework Helper

- 1,991

- 6

Generally this vector Ax will be some different vector, one that is linearly independent from v (it points in another direction). However if it is some scalar multiple of v (so [itex]Av=\lambda v[/itex] for some scalar [itex]\lambda[/itex] then v is called an eigenvector (the nullvector is ruled out as an eigenvector by definition) and [itex]\lambda[/itex] is its corresponding eigenvalue.

For example, if you take a vector in the plane R^2 and your linear transformation A is a rotation about the origin over 180 degrees, then every vector v will point in the opposite direction after the transformation, so Av=-v for all v. So every vector (not 0) is an eigenvector of A with eigenvalue -1.

- #3

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 967

Finding eigenvalues and eigenvectors is essentially finding for what vectors that matrix multiplication acts just like multiplying the vector by a number. It makes it possible to write the linear transformation as a sum of products of numbers,simplifying any problem involving that transformation.

Share: