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Linear Algebra and the C Language

This book provides a library for real matrices in C language.

The aim of this book is to provide real matrices in C language, to familiarize yourself with linear algebra.

Start by downloading the library (2 Hours!).

The next step is to study the properties and applications, once the entire library has been downloaded.

This book requires that you are familiar with C Programming.

This book requires that you are familiar with Linear Algebra.

This book requires that you are familiar with Octave Programming.

Properties and Applications: (The library)

Utilities for the C language

Utilities for the C language

Utilities for Octave

Working with matrices (M)

Basic operations on matrices (M)

Mathematic Applications: (M)

Identity matrix (M)
Triangular matrices (M)
Commutative matrices (M)
Similar matrices (M)
Symmetric matrices (M)
Skew-symmetric matrices (M)
Centrosymmetric matrices (M)
Positive-definite matrices (M)
Negative-definite matrices (M)
Hankel matrices (M)
Toeplitz matrices (M)
Taylor series: Exponential function (M)

Graphics Applications: (M)

The Transformation matrices [R2,C2] (M)

Determinant (Det)

Graphics Applications: (Det)

Graphics Applications: (TP)

Mathematic Applications: (TP)

Nonlinear systems (TP)
Choosing the solutions of the system (TP)

Gauss-Jordan Partial Pivoting (PP)

Gauss-Jordan Partial Pivoting (PP)
Free Variables (PP)

Applications: (PP)

Balancing a chemical equation (PP)

Mathematic Applications: (PP)

Find a basis for ... (PP)
Change of basis (PP)
Matrix of a linear application (PP)
Projection onto a vector subspace: (PP)
.
.
.
.

Dot product (Dp)

Orthonormal matrices (Q)

Orthonormal matrices (Q)
Some properties (Q)

QR Decomposition (QR)

QR Decomposition (QR)

Applications: (QR)

Network analysis (QR)
Analysis of an electrical circuit (QR)

Graphics Applications: (QR)

The coefficients of a polynomial (QR)
The coefficients of a conic (QR)
The coefficients of a circle (QR)
.

Eigenvalues Eigenvector (eigen)

Eigenvalues Eigenvector (eigen)
Some properties (eigen)
Eigenvalues with multiplicity (eigen)

Mathematic Applications: (eigen)

Condition number (eigen)
Matrix functions (eigen)
Linear discrete dynamical system (eigen)
The spectral decomposition (eigen)

Graphics Applications: (eigen)

The Quadratic forms: M[R2,C2] (eigen)
The Quadratic forms: M[R3,C3] (eigen)
Choose your eigenvalues (eigen)
The Projection of a plane (1) (eigen)
The Projection of a plane (2) (eigen)
The Projection of a space (1) (eigen)
The Projection of a space (2) (eigen)
The Projection of an hyperspace (1) (eigen)
The Projection of an hyperspace (2) (eigen)

The singular values (SVD)

The singular values (SVD)

SVD: Rn ≥ Cn

SVD: Rn ≥ Cn (SVD)
Some properties (SVD)

SVD: Cn > Rn

SVD: Cn > Rn (SVD)
.

Pseudo-Inverse

Pseudo-Inverse

Applications: (Pseudo-Inverse)

Network analysis (Left inverse)
Analysis of an electrical circuit (Left inverse)

Graphics Applications: (Pseudo-Inverse)

The coefficients of a polynomial (Left inverse)
The coefficients of a conic (Left inverse)
The coefficients of a circle (Left inverse)

The library

The library's construction is not standard. You can compile the C file directly. The functions are in the h files.

To access to the library, be sure to use #include "v_a.h" in the C source files.


Utilities Utilities Matrices Creation of matrices Print matrices Random matrices. Copy matrices. Basic operations on matrices Determinant Determinant .	Gauss-Jordan Total Pivoting (TP) Partial Pivoting (PP) Total Pivoting (TP) (Free variables) Partial Pivoting (PP) (Free variables) L'inverse with GaussJordan Dot product QR. Eigenvalue. Singular value Eigenvector SVD : Matrices with more rows than columns SVD : Matrices with more columns than rows

Gnuplot

Gnuplot

Contents

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