3 ms·
And they exist in situations where determinants are difficult or impossible to define! Infinite dimensional vector spaces can still have transformations with ei
by tgb 8y ago
And they exist in situations where determinants are difficult or impossible to define! Infinite dimensional vector spaces can still have transformations with eigenvectors but you generally can't define a determinant coherently for them (certainly they might have infinitely many eigenvalues and if the determinant is the product, then you have convergence problems). A classic example is that the standard Gaussian distribution is an eigenvector of the Fourier transform.
- in9 8y agoYou just blew my mind with this comment. I'm a statistics undergrad student and I really need to up my math knowledge. Where is this fact from? Functional analysis?
- tgb 8y agoYeah that would be a good course to learn it - functional analysis is basically linear algebra on infinite dimensional vector spaces. (Though that sells it a little short - moving to infinite dimensional vector spaces requires incorporating some topology too.)