Ad
related to: inverse matrix formula with answers pdf word converter ove pdf to doc textsodapdf.com has been visited by 100K+ users in the past month
Search results
Results From The WOW.Com Content Network
Let A be a square n-by-n matrix over a field K (e.g., the field of real numbers). The following statements are equivalent, i.e., they are either all true or all false for any given matrix: [3] A is invertible, i.e. it has an inverse under matrix multiplication, i.e., there exists a B such that AB = I n = BA. (In that statement ...
A matrix (in this case the right-hand side of the Sherman–Morrison formula) is the inverse of a matrix (in this case +) if and only if = =. We first verify that the right hand side ( Y {\displaystyle Y} ) satisfies X Y = I {\displaystyle XY=I} .
In mathematics, and in particular linear algebra, the Moore–Penrose inverse + of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [1] It was independently described by E. H. Moore in 1920, [2] Arne Bjerhammar in 1951, [3] and Roger Penrose in 1955. [4]
A variant of Gaussian elimination called Gauss–Jordan elimination can be used for finding the inverse of a matrix, if it exists. If A is an n × n square matrix, then one can use row reduction to compute its inverse matrix, if it exists. First, the n × n identity matrix is augmented to the right of A, forming an n × 2n block matrix [A | I]
A common case is finding the inverse of a low-rank update A + UCV of A (where U only has a few columns and V only a few rows), or finding an approximation of the inverse of the matrix A + B where the matrix B can be approximated by a low-rank matrix UCV, for example using the singular value decomposition.
Download as PDF; Printable version; In other projects ... Redirect to: Invertible matrix; Retrieved from ... Text is available under the Creative Commons Attribution ...
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
This gives a formula for the inverse of A, provided det(A) ≠ 0. In fact, this formula works whenever F is a commutative ring, provided that det(A) is a unit. If det(A) is not a unit, then A is not invertible over the ring (it may be invertible over a larger ring in which some non-unit elements of F may be invertible).