. Just a small note. I am exactly like this guy. EXACTLY. Will Mackenzie. Kinda bad looking. Bad teeth. Unremarkable complexion. High morals which have been discarded only too often. And an idealism-fuelled self assurance.   I used to think I was a lot like my girlfriend. But I think everyone knows she’s too good

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A continuation of the previous post

Let be an n-dimensional vector space, and let be a surjective linear mapping. If is m-dimensional, then is a matrix of order . Is it possible that ? Let us assume that it is. Then has a basis , all of which are mapped to by distinct vectors in . Moreover, these vectors have to

Dual spaces- An exposition

Studying Dual Spaces can be confusing. I know it was for me. I’m going to try to break down the arguments into a more coherent whole. I am following Serge Lang’s “Linear Algebra” (the Master is my favourite author). However, I am not strictly following the order he follows to develop the theory. Say we