Treatments for Vector Spaces, Spans, Bases and Projections - A First Course in Linear Algebra (II)
Last week, we introduced linear algebraic treatments to linear system with focus on computational methods. The focus is on solving systems, determinants and invertibility.
This week, we include further treatments to vector spaces, subspaces and linear spans/bases. We look at orthogonal/orthonormal sets, projections onto vector spaces, with applications in least-squares approximation and matrix factorization.
Within a few days, we will complete our treatment to linear systems in Euclidean spaces, covering diagonalizations of matrices and linear transformations. This will give us decent foothold over multivariate computations, from which we hope to leverage on to introduce discussions for portfolio management and multi-factor term structure models. We also release the formulaic alpha report in the days to come.
This linear algebra notes are available to all; the full market notes (476 pages) are available to paid readers only:
