The Living Thing / Notebooks :

Linear algebra

Oh! the hours I put in to studying the taxonomy and husbandry of matrices. Time has passed. I have forgotten much. Jacobians have begun to seem downright Old Testament.

And when you put the various operations of matrix calculus into the mix (derivative of trace of a skew-hermitian heffalump painted with a camel-hair brush) the combinatorial explosions of theorems and identities is intimidating. Now import general non-commutative algebraic structures.

Things I need to learn:

Basic linear algebra intros

Linear algebra and calculus

The multidimensional statistics/control theory workhorse.

Refs

Axle95
Axler, S. (1995) Down with Determinants!. The American Mathematical Monthly, 102(2), 139–154. DOI.
Axle14
Axler, S. (2014) Linear algebra done right. . New York: Springer
Dwye67
Dwyer, P. S.(1967) Some Applications of Matrix Derivatives in Multivariate Analysis. Journal of the American Statistical Association, 62(318), 607. DOI.
Gile08
Giles, M. B.(2008) Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation. In C. H. Bischof, H. M. Bücker, P. Hovland, U. Naumann, & J. Utke (Eds.), Advances in Automatic Differentiation (Vol. 64, pp. 35–44). Berlin, Heidelberg: Springer Berlin Heidelberg
MaAm14
Manton, J. H., & Amblard, P.-O. (2014) A Primer on Reproducing Kernel Hilbert Spaces. arXiv:1408.0952 [Math].
Mink00
Minka, T. P.(2000) Old and New Matrix Algebra Useful for Statistics.
Parl00
Parlett, B. N.(2000) The QR Algorithm. Computing in Science & Engineering, 2(1), 38–42. DOI.
PePe12
Petersen, K. B., & Pedersen, M. S.(2012) The Matrix Cookbook.