For any given complex matrix, it is possible to define many possible pseudoinverses. Let us try an example: How do we know this is the right answer? Pseudo inverse matrix. If A is a square matrix, we proceed as below: The term generalized inverse is sometimes used as a synonym of pseudoinverse. Active 7 years, 9 months ago. The pseudoinverse A + (beware, it is often denoted otherwise) is a generalization of the inverse, and exists for any m × n matrix. The Pseudo Inverse of a Matrix The Pseudo inverse matrix is symbolized as A dagger. Set the matrix (must be square) and append the identity matrix of the same dimension to it. To calculate inverse matrix you need to do the following steps. However, sometimes there are some matrices that do not meet those 2 … See the excellent answer by Arshak Minasyan. Here, A + A=I holds. 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). Let the system is given as: We know A and , and we want to find . 2x2 Matrix. Ask Question Asked 7 years, 9 months ago. The most commonly encountered pseudoinverse is the Moore-Penrose matrix inverse, which is a special case of a general type of pseudoinverse known as a matrix 1-inverse. pseudo-inverse of a matrix, and give another justification of the uniqueness of A: Lemma 11.1.3 Given any m × n-matrix A (real or complex), the pseudo-inverse A+ of A is the unique n×m-matrix satisfying the following properties: AA+A = A, A+AA+ = A+, (AA+)$ = AA+, (A+A)$ = A+A. If m