Linked Questions

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1answer
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
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1answer
885 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....
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1answer
445 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 ...
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0answers
388 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 ...
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0answers
180 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?
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0answers
162 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 ...
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0answers
149 views

Significance of eigen values [duplicate]

What is the significance/geometric interpretation of eigen values or eigen vectors in a vector space?
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0answers
121 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 ...
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1answer
69 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 ...
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4answers
70k 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 ...
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5answers
50k views

Real life examples for eigenvalues / eigenvectors

There are already good answers about importance of eigenvalues / eigenvectors, such as this question and some others, as well as this Wikipedia article. I know the theory and these examples, but now ...
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2answers
1k views

How to understsand eigenvalues and eigenvectors.

I know basic linear algebra (what is a matrix, what is a determinant, what is a square matrix, what is an inverse of a matrix, how to add/sub/multiple matrices etc.) But I am finding the concept of ...
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1answer
1k views

Interpretation of Matrix Diagonalization

If $A$ be a non singular matrix then what good does it do by constructing another matrix, say $P$ whose columns are a basis that consists of eigenvectors of $A$? Does it have something to do with ...
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2answers
1k views

How can eigenvectors and eigenvalues possibly be so useful?

I'm having a hard time trying to pin down why calculating the eigenvectors and eigenvalues of a matrix almost always gives something useful. There are numerous answers here on SX that discuss how to ...
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2answers
995 views

Significance and physical meaning of diagonalization of linear maps and bilinear forms, eigenvalues and eigenvectors

In linear algebra, I have studied the diagonalization of a linear map and of a bilinear form; and also the concepts of eigenvalues and eigenvectors. However, the importance of diagonalizing a linear ...

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