The survey talk "Complexity Classes and Linear Algebra"
by Eric Allender (Rutgers University) covered material
that is discussed in greater depth in the following papers:

Eric Allender
Making computation count: Arithmetic circuits in the Nineties, 
in the Complexity Theory Column, edited by Lane Hemaspaandra, SIGACT NEWS 28, 4
(December, 1997) pp. 2-15. 

Eric Allender, V Arvind and Meena Mahajan
Arithmetic Complexity, Kleene Closure, and Formal Power Series, 
submitted for journal publication.

Eric Allender, Robert Beals and Mitsunori Ogihara
The complexity of matrix rank and feasible systems of linear equations 
Computational Complexity, Vol. 8, 1999, 99-126.

Eric Allender, Klaus Reinhardt and Shiyu Zhou
Isolation, Matching, and Counting: Uniform and Nonuniform Upper Bounds, 
Journal of Computer and System Sciences 59 (1999) 164-181.

Eric Allender and Mitsunori Ogihara
Relationships among PL, #L, and the determinant 
RAIRO - Theoretical Informatics and Applications Vol. 30, 1996, pp. 1-21.

Alina Beygelzimer and Mitsunori Ogihara
On the Enumerability of the Determinant and the Rank 
University of Rochester Computer Science Technical Report 770. 
Available as ECCC Technical Report TR02-016 

Thanh Minh Hoang and Thomas Thierauf 
The Complexity of Verifying the Characteristic Polynomial and Testing 
Similarity 
Thanh Minh Hoang and Thomas Thierauf 
15th IEEE Conference on Computational Complexity (CCC), 87-95, 2000. 

Thanh Minh Hoang and Thomas Thierauf 
The Complexity of the Minimal Polynomial 
26th International Symposium on Mathematical Foundations of Computer Science 
(MFCS)  Springer Verlag, LNCS 2136, 408-420, 2001.

Thanh Minh Hoang and Thomas Thierauf 
On the Minimal Polynomial of a Matrix
To appear in COCOON'02

Thanh Minh Hoang and Thomas Thierauf 
The Complexity of the Inertia
Submitted

Meena Mahajan and V Vinay. 
Determinant: Old Algorithms, New Insights 
SIAM Journal on Discrete Mathematics 12(4): 474-490 (1999).

Meena Mahajan and V Vinay. 
Determinant: Combinatorics, Algorithms, and Complexity 
Chicago Journal of Theoretical Computer Science, Volume 1997 Article 5. 

Klaus Reinhardt and Eric Allender
Making nondeterminism unambiguous, 
SIAM J. Comp. Vol. 29, 2000, 1118-1131.

Miklos Santha and Sovanna Tan
Verifying the determinant in parallel, 
Computational Complexity 7:2, 128-151, 1998.

The papers of Eric Allender are available at 
http://www.cs.rutgers.edu/~allender/publications/