Analysis Tricks Part 1

I recently learnt a really neat trick when it comes to proving two quantities are equivalent. It started of with my supervisor claiming that for some and , (1)   is obvious. To me, it was not obvious at all, and may not be so obvious to you either. But what my...

The beautiful language of tensors

You’ve probably heard the word ‘tensor’ before, but if you’re like me, you’ve gone through your entire physics degree without knowing what they are. So today, I’m going to express the relativistic wave equation in the language of...

Real Projective Space and Quotient Spaces

So these spaces are really interesting, but super duper hard to get your head around. So in this blog, I hope to make there equivalent definitions a little bit easier to understand. I’m going to present 3 equivalent definitions of the n-dimensional real projective...

A voyage through space(s) (Part IV)

We have alas reached the final leg of our journey, we will continue with the idea of a normed vector space and then we will describe Banach spaces and Hilbert spaces. Associated with the norm on our vector space , is the metric     So is endowed with a...

A voyage through space(s) (Part III)

As promised, we begin our quest today in understanding what a normed vector space is. We will begin with a vector space , and we would like to give it some structure similar to our metric spaces. Now we could of course give any metric to , but we already have two...
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