Linear Algebra and the C Language
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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.
Contents
[edit | edit source ]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) 100% developed
[edit | edit source ]Working with matrices (M)
[edit | edit source ]- 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)
[edit | edit source ]- Basic operations (M)
- The trace function (M)
- The transpose function (M)
- .
Mathematic Applications: (M)
[edit | edit source ]- 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)
[edit | edit source ]Determinant (Det)
[edit | edit source ]- Determinant (Det)
- Elementary operations (Det)
- Intermediate functions (Det)
- Some properties (Det)
Graphics Applications: (Det)
[edit | edit source ]- 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)
[edit | edit source ]- The adjoint function (Det)
- The inverse with adjoint_mR(); (Det)
- The cross product function (Det)
- .
Gauss-Jordan Total Pivoting (TP)
[edit | edit source ]- Gauss-Jordan Total Pivoting (TP)
- The Inverse (TP)
Applications: (TP)
[edit | edit source ]Graphics Applications: (TP)
[edit | edit source ]- The coefficients of a polynomial (TP)
- The coefficients of a conic (TP)
- The coefficients of a circle (TP)
Mathematic Applications: (TP)
[edit | edit source ]Gauss-Jordan Partial Pivoting (PP)
[edit | edit source ]- Gauss-Jordan Partial Pivoting (PP)
- Free Variables (PP)
Applications: (PP)
[edit | edit source ]Mathematic Applications: (PP)
[edit | edit source ]- Find a basis for ... (PP)
- Change of basis (PP)
- Matrix of a linear application (PP)
- Projection onto a vector subspace: (PP)
- .
- .
- .
- .
Dot product (Dp)
[edit | edit source ]- Dot product (Dp)
- Some properties (Dp)
- Compute orthogonal vectors (Dp)
Orthonormal matrices (Q)
[edit | edit source ]- Orthonormal matrices (Q)
- Some properties (Q)
QR Decomposition (QR)
[edit | edit source ]- QR Decomposition (QR)
Applications: (QR)
[edit | edit source ]Graphics Applications: (QR)
[edit | edit source ]- The coefficients of a polynomial (QR)
- The coefficients of a conic (QR)
- The coefficients of a circle (QR)
Eigenvalues Eigenvector (eigen)
[edit | edit source ]- Eigenvalues Eigenvector (eigen)
- Some properties (eigen)
- Eigenvalues with multiplicity (eigen)
Mathematic Applications: (eigen)
[edit | edit source ]- Condition number (eigen)
- Matrix functions (eigen)
- The spectral decomposition (eigen)
Graphics Applications: (eigen)
[edit | edit source ]- 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)
[edit | edit source ]- The singular values (SVD)
SVD: Rn ≥ Cn
[edit | edit source ]- SVD: Rn ≥ Cn (SVD)
- Some properties (SVD)
SVD: Cn > Rn
[edit | edit source ]- SVD: Cn > Rn (SVD)
- .
Pseudo-Inverse
[edit | edit source ]Applications: (Pseudo-Inverse)
[edit | edit source ]- Network analysis (Left inverse)
- Analysis of an electrical circuit (Left inverse)
Graphics Applications: (Pseudo-Inverse)
[edit | edit source ]- The coefficients of a polynomial (Left inverse)
- The coefficients of a conic (Left inverse)
- The coefficients of a circle (Left inverse)
The library 100% developed
[edit | edit source ]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
[edit | edit source ]Matrices
[edit | edit source ]Determinant
[edit | edit source ]Gauss-Jordan
[edit | edit source ]- Total Pivoting (TP)
- Partial Pivoting (PP)
- Total Pivoting (TP) (Free variables)
- Partial Pivoting (PP) (Free variables)
- L'inverse with GaussJordan