Here you will find pages that employ JavaScript to effectuate simple calculations on matrices. In general a prompt box will ask for the dimensions and components of the matrices on which the calculations are to be carried out. The results of these calculations will then be displayed in a JavaScript generated page.

• Gaussian Elimination and Matrix Multiplication
  • Multiply a matrix A by a matrix B to form the product AB.
  • Multiply a matrix A by itself n times to form the product Aⁿ.
  • Carry out gaussian elimination on a n x m matrix A to reduce it to an echelon form with leading entries set to 1.
  • Carry out gaussian elimination and back substitution on a n x m matrix A and set leading entries to 1. In the case of a set of m linearly independent equations in m unknowns, Bx = c, if the matrix A is entered as A = B:c, the solution x will be represented explicitly in the form I:x where I is the identity matrix.
  • Calculate the inverse of a square matrix A. In this case gaussian elimination and back substitution are carried out on A:I yielding I:A^-1 when A is invertible.
  • Calculate the inverse of an m x m matrix A and if the inverse exists multiply it on the right by an m x n matrix B to form A^-1B.
• Calculate the determinant of a square matrix A.
  • The algorithm used simulates the procedure in which rows and columns of an m x m matrix are deleted to form m m-1 x m-1 matrices. This procedure is continued and finally terminates when m! 1 x 1 matrices are formed. The m! products, each composed of m terms, are formed. The sum of these products yields the determinant.
• Reduce a square matrix A to an echelon form and calculate the determinant.
  • In this case gaussian elimination is carried out on A:I. Multiplications and row interchanges are taken into account. Multiplying the diagonal entries of the resulting upper triangle matrix along with a number (-1)^k, where k is the number of row interchanges, yields the determinant of A.