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. __NOTOC__ 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 Cover Introduction + notice float:right;margin-left:10px;margin-right:0px; padding:5px;font-size:120%;line-height:120%; left This book requires that you are familiar with C Programming. notice float:right;margin-left:10px;margin-right:0px; padding:5px;font-size:120%;line-height:120%; left This book requires that you are familiar with Linear Algebra. notice float:right;margin-left:10px;margin-right:0px; padding:5px;font-size:120%;line-height:120%; left This book requires that you are familiar with Octave Programming. Properties and Applications: (The library) 100% + Utilities for the C language Utilities for the C language left image 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) . thumb| 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) 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 100% 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 L 100% Algebra University level mathematics books C programming language