Mathc,
Calculus Packages,
Vectors Packages,
Gnuplot Packages.
Presentation of the functions:
matrxf.zip
: You can work with fractions.
addm, subm, multm, powm, smultm, transpose, trace,
det, minor, mminor, cofactor, mcofactor, adjoint,
inverse(adjoint),inverse(gaussjordan),inverse(identity matrix),
gauss, gaussjordan, LU.
norm, distance, innerproduct,coldim, rowdim, rank,
nullity, leastsqrs
matrxg.zip
: You can also work with integers.
matrxh.zip
: The print, copy, rand, ... functions.
Copy and Past the code directly into Maple,
to verify the result.
You can do the same thing with c code,
and use this code in an another program.
matrxj.zip
: System of equations with the free variables.
In this section, the size of the matrices,
are randomly selected by the computer,
but you can selecte the size if you want.
Verify with numeric applications:
mtrxaa.zip
: How to use the basic functions.
when the size of the matrices are
randomly selected by the computer.
mtrxab.zip
: the properties of matrix arithmetic.
A+B = B+A
(A+B)+C = A+(B+C)
(AB)C = A(BC)
A(B+C) = AB+AC
(B+C)A = BA+CA
A(B-C) = AB-AC
(B-C)A = BA-CA
a(B+C) = aB+aC
a(B-C) = aB-aC
(a+b)C = aC+bC
(a-b)C = aC-bC
a(bC) = (ab)C
mtrxac.zip
:
* The properties of zero matrices.
* The properties of the transpose.
* The theorem of transpose.
* The theorem of inverse matrices.
mtrxad.zip
:
* (A+B)**2.
* (A-B)**2.
* (A-B) (A+B).
* Power and inverse.
* Symetric and Skew-Symetric matrices.
mtrxae.zip
:
* Solving linear systems by matrix inversions.
* Linear systems with common coefficient matrix.
mtrxaf.zip
:
* The system of equation Ax = b is consistent.
* Inverses of symmetric matrices.
* Power, inverse of diagonal matrices
* Multiply, inverse of triangular matrices.
* Trace property.
mtrxag.zip
: the value of the determinant of
* a diagonal matrix
* a triangular matrix (upper, lower)
* a basic matrix.
mtrxah.zip
: LU decomposition :
* LU decomposition.
* Det(A) = Det(L).
* invA = invU invL.
* LU decomposition are not unique.
Application:
mtrxid.zip
: Identity matrix application I
* Swap two rows.
* The pivot value.
* Eliminate the coefficient below, above, the pivot.
* Gauss Jordan elimination with the help of the identity matrix.
* Inverse of the matrix with the help of the identity matrix.
mtrxic.zip
: Identity matrix application II
* The work on a column in one step.
* All the values below the pivot in one step.
* Application : Gauss elimination.
* All the values above the pivot in one step.
* Application : Gauss Jordan elimination
* Application : Inverse of the matrix
mtrxgo.zip
: Geometric application.
You can verify the result into GnuPlot.
* Find the coefficients of a polynome,
that passes through three, four, five points.
* Find the coefficients a, b, c, d, e of a conic,
ax**2 + by**2 + cx + dy + e = 0
that passes through four points.
* Find the coefficients a, b, c, d of a circle,
a(x**2 + y**2) + bx + cy + d = 0
that passes through three points.
mtrxch.zip
: Chemistry application.
* Find the coefficients of a chemical equation.
mtrxsy.zip
: Resolve some nonlinear systems of equations.