- #1

orochimaru

i have trouble understanding these two terms.

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

Thks in advance!

- 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

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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

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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.

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