Mathc : This group work on numerical computation. You can find free source code to download.
Tutorial,
Calculus,
Linear Algebra,
Gnuplot. The other packages,
Complex : Language C (version 2003/10/09).
* You need a C compiler to compile the code (source).
* For this work, I use
Dev-C++ 4,
and
DJGPP two freewares.
* You can also use
Ch 4.0 released (C99).
The Standard Edition is free in all platforms.
* The graphic interface is gnuplot.
* You can download this freeware here : Gnuplot Central.
* My work is also a Freeware.
* Windows, Linux.
Complex Numbers.
cz01a.zip :
add, sub, multiply, divide, inverse, conjugate, symetric, abs.
Complex Matrices.
cm01a.zip :
add, subtract, multiply, conjugate, conjugate transpose, trace,
determinant, cofactor, matrix of cofactor, adjoint, inverse,
gauss, gaussjordan, LU decomposition, with complex values,
Euclidian inner product, norm, distance in C**n, in Mnm,
Verify with numeric applications:
cm03a.zip :
Vector space axioms on (rows, columns) vectors with complex coeffients.
cm03d.zip :
* The properties of the conjugate transpose.
* The theorem of the conjugate transpose.
* The theorem of inverse matrices.
* (A+B)**2, (A-B)**2, (A-B) (A+B).
cm03b.zip :
* Properties of Euclidian inner product in C**n.
* Properties of distance in C**n.
* u.v = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 + i/4 ||u+iv||**2 - i/4 ||u-iv||**2.
* If u.v =0 : ||u+v||**2 = ||u||**2 + ||v||**2.
cm03c.zip :
* Properties of inner product in Mmn with complex coefficients.
* Properties of distance in Mmn with complex coefficients.
* u.v = 1/4 ||u+v||**2 - 1/4 ||u-v||**2 + i/4 ||u+iv||**2 - i/4 ||u-iv||**2.
Application:
cm04a.zip :
Verify with numeric applications, some properties of the Dirac matrices..