Linear Algebra and the C Language

Wikibooks Contributors Present:
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.

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Contents

• Cover
• Introduction

Properties and Applications: (The library)

Utilities for the C language Utilities for the C language	Utilities for Octave Basic functions on matrices Write some basic matrices functions. Graphical utilities Examples of some applications Write your mathematics functions
Working with matrices (M) Create a matrix (M) Print a matrix (M) Print a matrix to a file (M) Print a matrix for Octave: (M) Copy a matrix (M) Random matrices (M) Choose Your Values (M) Array of matrices (M) Print row vectors: (M) Basic operations on matrices (M) Basic operations (M) The trace function (M) The transpose function (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) Determinant (Det) Elementary operations (Det) Intermediate functions (Det) Some properties (Det) Graphics Applications: (Det) The equation of a line (Det) The equation of a plan (Det) The equation of a parabola (Det) The equation of a circle (Det) The equation of a sphere (Det) Mathematic Applications: (Det) The adjoint function (Det) The inverse with adjoint_mR(); (Det) The cross product function (Det) .
Gauss-Jordan Total Pivoting (TP) Gauss-Jordan Total Pivoting (TP) The Inverse (TP) Applications: (TP) Network analysis (TP) Analysis of an electrical circuit (TP) Graphics Applications: (TP) The coefficients of a polynomial (TP) The coefficients of a conic (TP) The coefficients of a circle (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) Dot product (Dp) Some properties (Dp) Compute orthogonal vectors (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) 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