An Eigenvector is nothing more than a vector that points to some place. This pointing vector will th

Nylah Hendrix

Nylah Hendrix

Answered question

2022-07-02

An Eigenvector is nothing more than a vector that points to some place. This pointing vector will then be invariant under linear transformations.
Now my questions:
- Ok so this vector is invariant. So what? (in my case for attitude determination algorithm I even less understand what this could give me as useful information)
- how does a simple 4 × 4 matrix actually represent a transformation?

Answer & Explanation

alomjabpdl0

alomjabpdl0

Beginner2022-07-03Added 12 answers

No, an eigenvector is a vector that points to the same place after being transformed by the matrix.
As far as usefulness of eigenvectors go, it is very hard to find a mathematical concept that has more real life applications then the concept of eigenvectors: for example, the PageRank algorithm, which finds the dominant eigenvector of a matrix, is one of the most important parts in Google's algorithms for ranking webpages. Other examples include:
Quantum mechanics
Image recognition
Calculating frequencies of musical instruments
"Principal component analysis" in statistics
And many more. Each of these fields has it's own problems, but all of these problems can be translated into finding an eigenvector for a specific matrix. The "meaning" behind these vectors is then bestowed upon the solutions not by algebra ("pointing in the same direction"), but by the field that first had the problem!

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