Old and New Matrix Algebra Useful for Statistics
Thomas Minka
MIT Media Lab note (1997; revised 12/00)
A concise reference on advanced matrix theory, including:
- an easy way to compute matrix derivatives and second derivatives
- a general framework for inverting partitioned matrices
- useful properties of Kronecker product, Hadamard product, and diag
- the column-stacking operator "vec" and its generalization to
"vec-transpose"
with applications to multilinear models, principal component analysis,
blind source separation, Lyapunov equations, model alignment, and
more.
Matlab functions related to the paper (commutation matrix, duplication
matrix, etc) are available in a zip file.
PS .
PDF
Some other online references:
Thomas P Minka
Last modified: Mon Aug 22 18:02:27 GMT 2005