# pseudo inverse of a matrix

Here follows some non-technical re-telling of the same story. The inverse A-1 of a matrix A exists only if A is square and has full rank. Here, A + A=I holds. I is identity matrix. See the excellent answer by Arshak Minasyan. A + =(A T A)-1 A T satisfies the definition of pseudoinverse. The Pseudo Inverse of a Matrix The Pseudo inverse matrix is symbolized as A dagger. Property 1. Viewed 2k times 3 \$\begingroup\$ What is the step by step numerical approach to calculate the pseudo-inverse of a matrix with M rows and N columns, using LU decomposition? The term generalized inverse is sometimes used as a synonym of pseudoinverse. directly for a 2 £ 2 matrix, but not if A were 8 £ 3 or 10 £ 30. However, sometimes there are some matrices that do not meet those 2 … Reduce the left matrix to row echelon form using elementary row operations for the whole matrix (including the right one). If m n and if the inverse of A T A exists. where G † is the pseudo-inverse of the matrix G. The analytic form of the pseudo-inverse for each of the cases considered above is shown in Table 4.1. A solution of these questions can be found in general from the notion of a generalized inverse of a matrix: Deﬂnition. Well, for a 2x2 matrix the inverse is: In other words: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc). Active 7 years, 9 months ago. 1 Deﬂnition and Characterizations To calculate inverse matrix you need to do the following steps. Pseudo inverse matrix. For any given complex matrix, it is possible to define many possible pseudoinverses. If A is a square matrix, we proceed as below: Let the system is given as: We know A and , and we want to find . As a result you will get the inverse calculated on the right. The pseudoinverse A + (beware, it is often denoted otherwise) is a generalization of the inverse, and exists for any m × n matrix. If m