The Living Thing / Notebooks :

Linear algebra

If the thing is twice as big, the transformed version of the thing is also twice as big. {End}

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.

Things I need to learn:

Basic linear algebra intros

Linear algebra and calculus

The multidimensional statistics/control theory workhorse.

See matrix calculus.

Multilinear Algebra

Oooh you are playing wiht tensors? I don’t have a bunch to say here but here is a compact explanation of Einstein summation.


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. (2008a) An extended collection of matrix derivative results for forward and reverse mode automatic differentiation. Http://Eprints.Maths.Ox.Ac.Uk/1079.
Giles, M. B.(2008b) 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
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.