What Is an Eigenvalue?

Re:What Is an Eigenvalue? by geysersam on Tuesday November 08, 2022 @03:58PM (#33524206)

It's even worse than you describe it!

f needs to be linear, but the function in your example is not linear.

However, there are quite interesting linear functions. Example: f(x(t)) = x(t-2) + 4dx/dt - \int_0^t 2x(s) ds

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Re:What Is an Eigenvalue? by c-baby on Tuesday November 08, 2022 @03:59PM (#33524211)

5z + 2 is linear?

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Re:What Is an Eigenvalue? by lp251 on Tuesday November 08, 2022 @05:53PM (#33525405)

affine, not linear. describes a line that doesn't go through the origin. that pesky shift breaks linearity

5(2z) + 2 != 2(5z + 2)

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[dead]

Re:What Is an Eigenvalue? by Tainnor on Wednesday November 09, 2022 @01:14PM (#33535642)

All of linear algebra is based on linear functions. Of course that doesn't mean that you can't study affine functions with it, but it adds a layer of extra complication.

For example, linear functions over finite dimensional vector spaces can be represented with matrices which means that everything you can compute about matrices you can also compute about linear functions.

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Re:What Is an Eigenvalue? by xigoi on Wednesday November 09, 2022 @03:00AM (#33528609)

This is confusing terminology. Functions of the form ax+b are often called “linear”, but they're only linear in the general sense if b=0.

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