Linear Algebra and the 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.

To successfully work through this book, it is necessary to be familiar with the concepts of Linear Algebra presented and have a good foundation in C Programming.

• Introduction

• Utilities
• Utilities

• Matrices (M)
  • 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)
  • 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 coefficients of the equation of a line (Det)
    • The coefficients of the equation of a plan (Det)
    • The coefficients of the equation of a parabola (Det)
    • The coefficients of the equation of a circle (Det)
    • The coefficients of the equation of a sphere (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)
  • Free Variables (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)

• 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)

• Dot product (Dp)
• Dot product (Dp)
  • Some properties (Dp)

• Orthogonal matrix (Q)
• Orthogonal matrices (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)
  • Mathematic Applications: (eigen)
    • Matrix functions (eigen)
  • Graphics Applications: (eigen)
    • The Quadratic forms: M[R2,C2] (eigen)
    • The Quadratic forms: M[R3,C3] (eigen)
    • The Projection of a plane onto a line (eigen)
    • The Projection of a space onto a plan (eigen)
    • The Projection of a space onto a hyperplan (eigen)

• SVD: Rn ≥ Cn
• SVD: Rn ≥ Cn

• SVD: Cn > Rn
• SVD: Cn > Rn

• 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'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, or square matrices
  • SVD : Matrices with more columns than rows

• Octave: Matrices
• Octave: Functions
• Gnuplot