* Numeric and symbolic computation in C langage.
* You can find free source code to download.
Obsolete version. Work with real and complex values.
Linear Algebra (1) ... :
Fractions.
Linear Algebra (2) ... :
Floating Point.
Linear Algebra (2) ... :
C + GSL.
Linear Algebra (2) ... :
C + Octave.
New version. Work with real and complex values.
Linear Algebra (3) ... :
Algorithms, C+Octave
Statistics ................. :
A try.
Set .......................... :
Integer set, String set, Strings Set With Duplicate Elements
Symbolic ................. :
String (Derivative).
Symbolic ................. :
List (Symbolic algebra).
TeX ........................ :
Help.
Other ...................... :
Contes Et Legendes Du Comte De Nice
* You need a C compiler to compile the code (source).
* For this work, I use
Dev-C++ 4
a freeware.
* The graphic interface is
Gnuplot. (free)
* My work is also a Freeware.
* Windows, Linux.
hfile_r.zip : Download this package first. You can use this package with GSL, Octave
pow, smul, transpose, trace,det, minor, mminor,cofactor, mcofactor,
adjoint,inverse(adjoint), inverse(gaussjordan), gauss, gaussjordan,
LU, PLU, Gram-Schimdt process, householder, QR decomposition.
If you mix my work with the Octave functions, you can have :
pseudoinverse, Cholesky Decomposition, Hessenberg decomposition,
the singular value decomposition, schur decomposition.
You can use maple,
octave 2.1.42,
scilab 2.6,
Maxima 5.90,
to verify my functions.
* nba.zip :
Vector space axioms.
* nbb.zip :
The properties of matrix arithmetic.
* nbc.zip :
(A+B)**2, (A-B)**2, (A-B) (A+B).
* nbd.zip :
The properties of the conjugate transpose.
* nbe.zip :
Complex numbers.
* nbf.zip :
Trace.
Determinant, Inverse :
* nbi.zip :
Basic properties of determinant.
* nbj.zip :
Matrices (symmetric, diagonal, triangular).
* nbk.zip :
The theorem of the conjugate transpose.
* ........... : The theorem of inverse matrices
* nbl.zip :
Solving linear systems by matrix inversions.
* ........... : Linear systems with common coefficient matrix.
* ........... : The system of equation Ax = b is consistent.
* nbm.zip :
Power series representation of inv(I-A).
* ........... : Nilpotent matrices.
Linear equations :
* nbq.zip :
Reduced row-echelon form without introducing any fractions.
* nbr.zip :
A pivoting strategy (Partial, Complete Pivoting).
* nbs.zip :
Linear combination, dependant, independant, basis.
* nbt.zip :
Orthogonal complement., Nullspace, Row space, Column space.
* nbu.zip :
Linear systems with common coefficient matrix.
* nbv.zip :
Column-Row Factorization, Column-Row Expansion.
* nbw.zip :
A = uv_T, A = uu_T.
* nci.zip :
LU decompositions.(determinant, inverse, solving system of equations)
* ncj.zip :
PLU decompositions.(determinant, inverse, solving system of equations)
* nca.zip :
System of equations with free variables.
* ncd.zip :
System of equations with free variables. (complex variable)
* nck.zip :
Reflection about an axis. (Gnuplot).
* ........... : Reflection about the line y = x.
* ........... : Orthogonal projection on an axis.
* ........... : Dilatation and Contraction of a square.
* ........... : Shear in the x-direction with factor k.
* ncl.zip :
Vector2d (vertical horizontal shift).
* ncm.zip :
Reflection about a plan.
* ........... : Orthogonal projection on a plan.
Inner product, Length, Distance :
* nde.zip :
Euclidian Inner product, Length, Distance. (complex)
* ndf.zip :
Euclidian Inner product, Length, Distance. (real)
* ndg.zip :
Inner product in Mnm. (complex)
* ndh.zip :
Inner product in Mnm. (real)
* ndi.zip :
Inner Product on R**n generated by A.
* ndj.zip :
The Weighed Euclidean Inner Product.
* ndk.zip :
The Gram-Schmidt process. (complex)
* ndl.zip :
The Gram-Schmidt process. (real)
* ncw.zip :
properties of Orthogonal matrices.
* ncu.zip :
Least squares fit of a polynomial. (GnuPlot)
* ncv.zip :
The least squares and system of equations with QR decomposition.
* ncx.zip :
Householder matrices
Eigenvalue, Eigenvector,eigenspace :
* nco.zip :
Some properties of Eigenvalue, Eigenvector, Cayley-Hamilton theorem.
* ncp.zip :
Eigenspace, eigenvectors, eigenvalue.
* ncq.zip :
Compute the dominant eigenvalue.
* ncr.zip :
Compute the eigen value with the QR decomposition.
* ncs.zip :
Compute the eigen value with the Power method.
* nda.zip :
Functions of matrices :
* ........... : Trigonometric, Hyperbolic.
* ........... : If AB = BA then A and B commute.
Complex see gsl or octave packages.
* ndb.zip :
Some linear transformation
* ndc.zip :
Similarity invariants
* ndd.zip : Geometric applications. (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.