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Quantitative and Qualitative Treatments to Capital Markets; Notes on Abstract Linear Algebra (PART I)
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Quantitative and Qualitative Treatments to Capital Markets; Notes on Abstract Linear Algebra (PART I)

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HangukQuant
May 29, 2023
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HangukQuant Research
Quantitative and Qualitative Treatments to Capital Markets; Notes on Abstract Linear Algebra (PART I)
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In the previous notes, we talked portfolio management. As mentioned, we will develop abstract algebra theory in parallel. Last month, we did a complete treatment of linear algebra in Euclidean spaces:

Diagonalization and Linear Transformations - A First Course in Linear Algebra (III) - a complete first course in linear algebraic methods.

Diagonalization and Linear Transformations - A First Course in Linear Algebra (III) - a complete first course in linear algebraic methods.

HangukQuant
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April 16, 2023
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I am glad that many of the readers reached out to me and told me that they enjoyed my way of presentation and dense workings. I thank the readers who emailed me and corrected errata in some of the workings.

I am looking to complete the treatment for abstract linear algebra over a series of 3-5 posts (so it should be 1~2 months at most). The content covered would be similar to a full semester’s second course in linear algebra. So understandably our pace would be much faster than you might be used to; this is intentional. Again this would allow us to develop more in-depth discussions in practice, and gain intuition over problem-solving in high dimensional settings.

This week’s post is a gentle introduction to finite dimensional vector spaces, and extending from the concepts in the Euclidean space. Most of the proofs have parallels in our notes on Euclidean space algebra and hence shortened; additional concepts such as complex arithmetic, direct sums and polynomial function spaces are new. We will cover much more, and introduce completely new topics such as dual spaces in the coming posts. Once we are done with the series, I believe our readers should have a fairly deep appreciation for the mathematics of finite dimensional vector spaces.

Happy studying.

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