Re: Matrix Inverse Issue

*To*: mathgroup at smc.vnet.net*Subject*: [mg80600] Re: [mg80556] Matrix Inverse Issue*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sun, 26 Aug 2007 23:10:38 -0400 (EDT)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200708260700.DAA03587@smc.vnet.net>*Reply-to*: murray at math.umass.edu

If A and B are matrices of the same size, then A B is NOT the matrix product of A and B; rather, it is the matrix of that same size that you get by multiplying corresponding elements of A and B. Multiplication of numbers is Listable -- it extends to lists, and lists of lists, ..., when their dimensions permit it. The matrix product of two compatibly-sized matrices A and B is A.B, shorthand for Dot[A,B]. So Mathematica gave you precisely what you asked for. What you wanted -- and it could not read your mind -- is: A = Table[If[j==i, 1-i/10, If[j==i+1, i/10, 0]], {i, 9}, {j, 9}]; A.Inverse[A]==IdentityMatrix[9] True (I used the test for equality with identity matrix there to spare showing the multi-line output of the identity matrix.) Brian Gladman wrote: > I am having a problem with the matrix inverse for the following matrix in > Mathematica 6: > > A = Table[If[j == i, 1 - i/10, If[j == i + 1, i/10, 0]], {i, 9}, {j, 9}] > > {{9/10, 1/10, 0, 0, 0, 0, 0, 0, 0}, {0, 4/5, 1/5, 0, 0, 0, 0, 0, > 0}, {0, 0, 7/10, 3/10, 0, 0, 0, 0, 0}, {0, 0, 0, 3/5, 2/5, 0, 0, 0, > 0}, {0, 0, 0, 0, 1/2, 1/2, 0, 0, 0}, {0, 0, 0, 0, 0, 2/5, 3/5, 0, > 0}, {0, 0, 0, 0, 0, 0, 3/10, 7/10, 0}, {0, 0, 0, 0, 0, 0, 0, 1/5, 4/ > 5}, {0, 0, 0, 0, 0, 0, 0, 0, 1/10}} > > A Inverse[A] > > {{1, -1/72, 0, 0, 0, 0, 0, 0, 0}, {0, 1, -1/14, 0, 0, 0, 0, 0, 0}, {0, > 0, 1, -3/14, 0, 0, 0, 0, 0}, {0, 0, 0, 1, -8/15, 0, 0, 0, 0}, {0, > 0, 0, 0, 1, -5/4, 0, 0, 0}, {0, 0, 0, 0, 0, 1, -3, 0, 0}, {0, 0, 0, > 0, 0, 0, 1, -49/6, 0}, {0, 0, 0, 0, 0, 0, 0, 1, -32}, {0, 0, 0, 0, > 0, 0, 0, 0, 1}} > > I expected the identity matrix here but I get extra terms. > > Am I doing something wrong? > > Brian Gladman > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Matrix Inverse Issue***From:*"Brian Gladman" <brg@nowhere.org>