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Symmetric Matrices and Positive Definiteness

Symmetric matrices have three important properties that make it the ‘ideal’ matrix to have:

1.) Symmetric matrices satisfy 

2.) For a symmetric matrix with real entries, the eigenvalues are also real… 531 more words

Mathematics

Differential equations and exp(At)

How would you solve the following system of linear first order differential equations?

We can write this in matrix form:

Where and . Our first step is to write our system of differential equations in the form . 504 more words

Mathematics

'Diagonalisation' and the Fibonacci Sequence

We now know what eigenvalues and eigenvectors are and how to compute them but now what can we do with them? We will quickly see that the eigenvalues and eigenvectors offer a greater glimpse on the properties of matrix . 499 more words

Mathematics

Eigenvalues and Eigenvectors

Eigenvalues and eigenvectors appear everywhere: geology, image processing, Schrödinger’s Equation, atomic orbitals and so on. This is enough justification to study this unit.

So what are they? 411 more words

Mathematics

Working with base states and Hamiltonians

I wrote a pretty abstract post on working with amplitudes, followed by more of the same, and then illustrated how it worked with a practical example (the ammonia molecule as… 3,560 more words

Physics

On uncertainty (with cartoon ending).

Reading about the uncertainty principle in popular literature almost always sets my teeth on edge.

I assume most people have a few qualms like that, things they often see done incorrectly that infuriate them.  3,274 more words

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