Quantitative and Qualitative Treatments to Capital Markets; 660 pages; Notes on Abstract Linear Algebra (PART IV)
Preview of Notes
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Last week we studied polynomials, eigenvectors and invariant subspaces, inner product spaces, upper and diagonal matrices et cetera. This week, we take a look at operators on the inner product space, investigating practically important linear maps such as self-adjoint, positive semidefinite and isometric operators, as well as techniques such as polar decomposition and singular value decomposition useful in computational algebra.
This leaves two more notes in our abstract linear algebra series. We are nearing the end of our second year on the HangukQuant blog, where we transitioned to being more engaged in discussing the practice of quantitative research, rather than the end product alone. To recap, we began with sharing useful code such as engineering data service layers, performance profiling backtest engines and designing credit API throttlers using a semaphore:
and then introduced some interesting papers on quant alpha modelling and strategy development:
Also, we looked at enhancing our quant library with some useful tools:
while developing and compiling the scientific theory behind the math and statistical methods driving quantitative research:
Moving forward into the next year, we hope to continue the tango between theory and practice of quantitative methods. While we are on a roll, we hope to cover convex optimization theory, which will utilize many concepts discussed in the linear algebra series. We will then come full circle to start our coding series again, developing more advanced quant libraries in Python.
Market Notes (paid):