4k views

### Why we need eigenvectors and eigenvalues [duplicate]

Given a matrix A, what do eigenvectors and eigenvalues of A imply? I know how to calculate them but I want to understand WHY do we need to find them? In what application this is important Thank you
2k views

### What exactly do eigenvalue and eigenvector indicate? [duplicate]

What exactly do eigenvalue and eigenvector indicate? I mean what is the importance in calculating them. We all know how to calculate them but I do not know the exact importance
1k views

### Diagonalization: Eigenvalues Vs Elementary Row Operations [duplicate]

Using elementary row operations, a matrix A $\in \mathrm{R}^{n \times n}$ can be reduced to a Row-Reduced Echelon (RRE) form. Using the RRE form of A, the bases of Nullspace and Range can be obtained....
607 views

### Why are Eigenvalues So Important? [duplicate]

I understand the definition of eigenvalues and eigenvectors. Eigenvectors just stretch when applied by a linear transformation (a matrix). So far so good. I am surprised by the amount of times they ...
417 views

### What is an Eigenvector? [duplicate]

I am taking differential equations in college right now and lately we have been working on eigen values and vectors. Beyond all the math I'm trying to conceptualize what is going on when you attain a ...
202 views

### Why should I care about eigenvectors/eigenvalues [duplicate]

I've been studying pattern recognition/machine learning and the theory behind it for some time now and I notice that I find myself seeing the same things over and over again, yet without fully ...
72 views

### What are eigenvectors all about? [duplicate]

It's awkward, but to be completely honest: I never understood what eigenvectors are all about. The only reasons I can think of why they could be interesting are: They are calculated to diagonalize a ...
197 views

### What is the importance of eigenvalues in mathematics ? In the real world, where we use them? [duplicate]

What is the importance of eigenvalues in mathematics? In the real world, where do we use these eigenvalues?
160 views

### Significance of eigen values [duplicate]

What is the significance/geometric interpretation of eigen values or eigen vectors in a vector space?
132 views

### What is the meaning of the eigenvector and eigenvalue ? Why is that so interesting/important? [duplicate]

I asked many people those questions and everybody can calculate the eigenvector and eigenvalue of a given example, but if I ask those people what does it mean I always see frozen faces and and get an ...
81 views

### Usage of Eigenvalue and Eigenvector [duplicate]

I have been working with factor and cluster analysis where I found the introduction of Eigenvalue. So, I read about it and I have understood the idea how to find it but still, I am unable to see the ...
135k views

### Real world application of Fourier series

What are some real world applications of Fourier series? Particularly the complex Fourier integrals?
74k views

### A simple explanation of eigenvectors and eigenvalues with 'big picture' ideas of why on earth they matter

A number of areas I'm studying in my degree (not a maths degree) involve eigenvalues and eigvenvectors, which have never been properly explained to me. I find it very difficult to understand the ...