This method demands many operations and clearly includes more round-off errors. The fundamental partitioning method of Greville for calculating generalized inverses was discussed in. The terms “the minimum-norm least squares inverse,” “the Moore-Penrose inverse,” and “the pseudo-inverse” of a matrix are much more used than the term “Drazin inverse.” This unique inverse is globally used for solving linear systems and linear optimization problems. Kahan (1965) are just a couple of names who have contributed significantly in the area of generalized matrix inverse and its applications leaving very little scope for others to contribute in this area. But intense activities started since 1955. Moore (1920) was a pioneer in the area of a generalized algebraic matrix inverse. Enormous amount of work in the topic of generalized inverses has been done during the past 63 years. Methods for calculating the generalized inverses are a topic of current investigation in computational mathematics (see, e.g., ). The theoretical discussions are upheld by several experiments showing the stability and convergence of the proposed method. The convergence is investigated analytically by applying a suitable initial matrix. The objective of this work is to propose a computationally effective iterative scheme for finding the Drazin inverse. Replace a row by the sum of itself and a constant multiple of another row of the matrix.Drazin inverse is one of the most significant inverses in the matrix theory, where its computation is an intensive and useful task.Multiply each element of row by a non-zero integer.The following row operations are performed on augmented matrix when required:.Perform the row reduction operation on this augmented matrix to generate a row reduced echelon form of the matrix.Form the augmented matrix by the identity matrix.In order to find the inverse of the matrix following steps need to be followed: Steps to find the inverse of a matrix using Gauss-Jordan method: Gauss-Jordan Method is a variant of Gaussian elimination in which row reduction operation is performed to find the inverse of a matrix.

Minors, Cofactors and Ad-jugate Method (Inefficient)Įlementary Row Operation (Gauss – Jordan Method):.Elementary Row Operation (Gauss-Jordan Method) (Efficient).Methods for finding Inverse of Matrix:įinding the inverse of a 2×2 matrix is a simple task, but for finding the inverse of larger matrix (like 3×3, 4×4, etc) is a tough task, So the following methods can be used: Where, Adj(A) denotes the adjoint of a matrix and, Det(A) is Determinant of matrix A. In general, the inverse of n X n matrix A can be found using this simple formula: There exist an Identity matrix I for which.The matrix must be a non-singular matrix and,.The inverse of a matrix is only possible when such properties hold: Given a square matrix A, which is non-singular (means the Determinant of A is nonzero) Then there exists a matrix Operations that can be performed on a matrix are : Addition, Subtraction, Multiplication or Transpose of matrix etc. Matrix is an ordered rectangular array of numbers. The C++ Standard Template Library (STL).Map in C++ Standard Template Library (STL).Initialize a vector in C++ (7 different ways).Print unique rows in a given Binary matrix.Rotate a matrix by 90 degree in clockwise direction without using any extra space.Rotate a matrix by 90 degree without using any extra space | Set 2.Inplace rotate square matrix by 90 degrees | Set 1.Print a given matrix in counter-clock wise spiral form.Mathematics | Eigen Values and Eigen Vectors.Mathematics | System of Linear Equations.Mathematics | L U Decomposition of a System of Linear Equations.Gaussian Elimination to Solve Linear Equations.Program for Gauss-Jordan Elimination Method.Finding inverse of a matrix using Gauss – Jordan Method | Set 2.ISRO CS Syllabus for Scientist/Engineer Exam.ISRO CS Original Papers and Official Keys.GATE CS Original Papers and Official Keys.

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