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.


Axler, S. (1995) Down with Determinants!. The American Mathematical Monthly, 102(2), 139–154. DOI.
Axler, S. (2014) Linear algebra done right. . New York: Springer
Dwyer, P. S.(1967) Some Applications of Matrix Derivatives in Multivariate Analysis. Journal of the American Statistical Association, 62(318), 607. DOI.
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
Manton, J. H., & Amblard, P.-O. (2014) A Primer on Reproducing Kernel Hilbert Spaces. arXiv:1408.0952 [Math].
Minka, T. P.(2000) Old and New Matrix Algebra Useful for Statistics.
Parlett, B. N.(2000) The QR Algorithm. Computing in Science & Engineering, 2(1), 38–42. DOI.
Petersen, K. B., & Pedersen, M. S.(2012) The Matrix Cookbook.