(Matrix * BiVector) Multiplication Timing Results:
 
Non-optimized builds (SRT_QUAL = default) Optimized builds (SRT_QUAL = maxopt)
5x5 Matrix 6x6 Matrix 5x5 Matrix 6x6 Matrix
LinearAlgebra 
Matrix * Matrix (*)
Matrix not specialized
Matrix not declared symmetric
[tsnmul10]
Min: 4.39 secs (4.39 µsecs)
Max: 4.48 secs (4.48 µsecs)
Min: 5.51 secs (5.51 µsecs)
Max: 5.68 secs (5.68 µsecs)
Min: 4.3 secs (4.3 µsecs)
Max: 4.4 secs (4.4 µsecs)
Min: 5.5 secs (5.5 µsecs)
Max: 5.65 secs (5.65 µsecs)
LinearAlgebra
Matrix * Matrix (*)
Matrix not specialized
Matrix declared symmetric
[tsnmul10]
Min: 6.6 secs (6.6 µsecs)
Max: 6.8 secs (6.8 µsecs)
Min: 8.28 secs (8.28 µsecs)
Max: 8.51 secs (8.51 µsecs)
Min: 6.65 secs (6.65 µsecs)
Max: 6.97 secs (6.97 µsecs)
Min: 8.35 secs (8.35 µsecs)
Max: 8.59 secs (8.59 µsecs)
LinearAlgebra
Matrix * Matrix (*)
Matrix specialized
Matrix not declared symmetric
[tsnmul10]
Min: 3.26 secs (3.26 µsecs)
Max: 3.34 secs (3.34 µsecs)
Min: 3.68 secs (3.68 µsecs)
Max: 3.77 secs (3.77 µsecs)
Min: 3.29 secs (3.29 µsecs)
Max: 3.6 secs (3.6 µsecs)
Min: 3.67 secs (3.67 µsecs)
Max: 3.9 secs (3.9 µsecs)
LinearAlgebra
Matrix * Matrix (*)
Matrix specialized
Matrix declared symmetric
[tsnmul10]
Min: 6.72 secs (6.72 µsecs)
Max: 6.85 secs (6.85 µsecs)
Min: 8.82 secs (8.82 µsecs)
Max: 8.95 secs (8.95 µsecs)
Min: 6.7 secs (6.7 µsecs)
Max: 7.05 secs (7.05 µsecs)
Min: 8.82 secs (8.82 µsecs)
Max: 9.26 secs (9.26 µsecs)
CLHEP
HepMatrix * HepMatrix (**)
[tsnmul11]
Min: 3.67 secs (3.67 µsecs)
Max: 3.75 secs (3.75 µsecs)
Min: 4.61 secs (4.61 µsecs)
Max: 4.66 secs (4.66 µsecs)
Min: 3.45 secs (3.45 µsecs)
Max: 3.58 secs (3.58 µsecs)
Min: 4.54 secs (4.54 µsecs)
Max: 4.6 secs (4.6 µsecs)
CLHEP
HepSymMatrix * HepMatrix (**)
[tsnmul12]
Min: 5.6 secs (5.6 µsecs)
Max: 5.74 secs (5.74 µsecs)
Min: 7.15 secs (7.15 µsecs)
Max: 7.34 secs (7.34 µsecs)
Min: 5.53 secs (5.53 µsecs)
Max: 5.71 secs (5.71 µsecs)
Min: 7.2 secs (7.2 µsecs)
Max: 7.38 secs (7.38 µsecs)
CovMatrices (***)
CovMatrixX * BiVectorX
[tsnmul13]
Min: 0.52 secs (0.52 µsecs)
Max: 0.54 secs (0.54 µsecs)
Min: 0.67 secs (0.67 µsecs)
Max: 0.69 secs (0.69 µsecs)
Min: 0.48 secs (0.48 µsecs)
Max: 0.54 secs (0.54 µsecs)
Min: 0.66 secs (0.66 µsecs)
Max: 0.71 secs (0.71 µsecs)

All timings are based on 1,000,000 multiplications.
The first number is the time for all the inversions while the time in parenthesis is the time for 1 multiplication.
The string in the bracket is the name of the test module build for the particular test.
When the results say "Non-Optimized builds," then all the libraries and the test module were build with the "SRT_QUAL" variable having the "default" value.
When the results say "Optimized builds," then all the libraries and the test module were build with the "SRT_QUAL" variable having the "maxopt" value.

(*) Since we can't do Matrix * BiVector in LinearAlgebra , we did Matrix * Nx2 Matrix.
(**) Since we can't do Matrix * BiVector in CLHEP, we did HepMatrix * Nx2 HepMatrix.
(***) Covariant Matrices are inherently symmetric.
 

Matrices and Vectors used in the tests:

LinearAlgebra:
5x5 matrix
     1e+03                    4                    6                    8                  10
             4         1.1e+03                  16                  18                  20
             6                  16         1.2e+03                  28                  30
             8                  18                  28         1.3e+03                  40
           10                  20                  30                  40         1.4e+03
10-element "bivector":
         2               4
         4               6
         6               8
         8             10
       10             12
6x6 matrix:
     1e+03                    4                    6                    8                  10                  12
             4         1.1e+03                  18                  20                  22                  24
             6                  18         1.2e+03                  32                  34                  36
             8                  20                  32         1.3e+03                  46                  48
           10                  22                  34                  46         1.4e+03                  60
           12                  24                  36                  48                  60         1.5e+03
12-element "bivector":
          2                4
          4                6
          6                8
          8              10
        10              12
        12              14

CLHEP:
5x5 matrix:
         1000                4               6                8               10
               4          1100              16              18              20
               6              16          1200              28              30
               8              18              28          1300              40
             10              20              30              40          1400
10-element "bivector":
          2                4
          4                6
          6                8
          8              10
        10              12
6x6 matrix:
         1000                4                6                8              10              12
               4          1100              18              20              22              24
               6              18          1200              32              34              36
               8              20              32          1300              46              48
             10              22              34              46          1400              60
             12              24              36              48              60          1500
12-element "bivector":
          2                4
          4                6
          6                8
          8              10
        10              12
        12              14

CovMatrices:
5x5 matrix:
 +1.0000000000e+03
  +4.0000000000e+00   +1.1000000000e+03
  +6.0000000000e+00   +1.6000000000e+01   +1.2000000000e+03
  +8.0000000000e+00   +1.8000000000e+01   +2.8000000000e+01   +1.3000000000e+03
  +1.0000000000e+01   +2.0000000000e+01   +3.0000000000e+01   +4.0000000000e+01   +1.4000000000e+03
10-element bivector:
  +2.0000000000e+00   +4.0000000000e+00   +6.0000000000e+00   +8.0000000000e+00   +1.0000000000e+01
  +2.0000000000e+00   +4.0000000000e+00   +6.0000000000e+00   +8.0000000000e+00   +1.0000000000e+01
6x6 matrix:
 +1.0000000000e+03
  +4.0000000000e+00   +1.1000000000e+03
  +6.0000000000e+00   +1.8000000000e+01   +1.2000000000e+03
  +8.0000000000e+00   +2.0000000000e+01   +3.2000000000e+01   +1.3000000000e+03
  +1.0000000000e+01   +2.2000000000e+01   +3.4000000000e+01   +4.6000000000e+01   +1.4000000000e+03
  +1.2000000000e+01   +2.4000000000e+01   +3.6000000000e+01   +4.8000000000e+01   +6.0000000000e+01   +1.5000000000e+03
12-element bivector:
  +2.0000000000e+00   +4.0000000000e+00   +6.0000000000e+00   +8.0000000000e+00   +1.0000000000e+01   +1.2000000000e+01
  +2.0000000000e+00   +4.0000000000e+00   +6.0000000000e+00   +8.0000000000e+00   +1.0000000000e+01   +1.2000000000e+01
 

Testing system specs:

CPU: 500 MHz PentiumIII (Katmai)
Memory: 128MB SDRAM
Cache: 512KB
Hard Disk: IBM 13677MB
Video Card: 16MB Diamond Viper TNT 1.95E

OS: Fermi Linux Release 6.1.1 (Strange)
Kernel: 2.2.16-3 on an i686
X-Server: XFree86 Version 11.0 Release 3360

Tests were compiled and build using GCC 3.0.1

Nick Macks