Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
See also: linear equations, equivalence operations  
GaussJordan Algorithm
The GaussJordan algorithm can be used to solve linear equations and/or to calculate the inverse of a matrix. The GaussJordan algorithm is based on equivalence operations. While this algorithm is easy to understand, it is not the best way to solve linear equations, since it takes up to three times longer than the best algorithms available, and requires additional storage space.
As an example, suppose you have to solve the following system of linear equations: First, we have to align the unknown variables. Variables which are not used in a particular equation are entered with a coefficient of zero: From this aligned system of equations we extract the coefficients on the left side, and the constants on the right side (blue) to form a rectangular matrix: If we need for some reason the inverse of the coefficient matrix, we also have to add the identity matrix (red), so that we finally start with the following matrix: In order to solve this system, we have to apply equivalence operations in such a way that the black square submatrix becomes the identity matrix. In doing so, we obtain the following matrix: Now the blue vector contains the solutions, and the red former identity matrix contains the inverse of the original (black) coefficient matrix. Thus, the solution of the system of linear equations is: x_{1} = 2


Last Update: 20121008