MaplePrimes - answers and comments on Question, matrix multiplication error

lists and Matrices

pagan — Mon, 06 Feb 2012 08:42:34 Z

Judging by (what I hope is) text representation of your output, it looks like you might have accidentally created your Matrices with the wrong orientations. Doing A.B for A a 2x1 Matrix and B a 1x2 Matrix will compute an outer product and result in a 2x2 Matrix.

This works for me

> restart:

> b2 := zeta -> Matrix([[-y(zeta)], [-x(zeta)]])^%T:

> N0 := zeta -> Matrix([[(1-zeta)], [(zeta)]]):

> b2(zeta); # 1x2

                            [-y(zeta)  -x(zeta)]

> N0(zeta); # 2x1

                                 [1 - zeta]
                                 [        ]
                                 [  zeta  ]

> b2(zeta) . N0(zeta); # 1x1

                    [-y(zeta) (1 - zeta) - x(zeta) zeta]

I don't understand why you're creating b2, N0, and B2 as operators instead of expressions, if you're just going to use them by applying them to the name zeta. It's also a bit unclear whether you mean -x*zeta or -x(zeta) a function application. And did you make a typographic error, using `be` instead of `b2`?

It looks like you might have accidentally done this. Notice the difference in the bracketing inside the calls to the Matrix constructor.

> restart:

> b2 := zeta -> Matrix([[-y(zeta), -x(zeta)]])^%T;

                                                      %T
                    b2 := zeta -> [-y(zeta)  -x(zeta)]  

> N0 := zeta -> Matrix([[(1-zeta), (zeta)]]);

                       N0 := zeta -> [1 - zeta  zeta]

> b2(zeta); # 2x1

                                 [-y(zeta)]
                                 [        ]
                                 [-x(zeta)]

> N0(zeta); # 1x2

                              [1 - zeta  zeta]

> b2(zeta) . N0(zeta); # 2x2

                    [-y(zeta) (1 - zeta)  -y(zeta) zeta]
                    [                                  ]
                    [-x(zeta) (1 - zeta)  -x(zeta) zeta]

Thank you very much for your help. I needed

serena88 — Mon, 06 Feb 2012 22:34:10 Z

Thank you very much for your help. I needed the first scenario, i left it as an operator because i need to differentiate and integrate it later on.

Add on question to Matrix dot product

serena88 — Tue, 14 Feb 2012 18:26:53 Z

Hi, I have another add on question regarding the dot product of matrix :

with(LinearAlgebra):

A:=Matrix([[3,t,2f],[k,4,w]]) ###2x3 matrix

B:=Matrix([[g],[h],[m]]) ###3x1 matrix

Method 1 : why can I not get "DotProduct(A,B)"?

Method 2: but when I put down "A.B", it gives me the answer.

I try again with C:=Matrix([[a,b]]) ###1x2 matrix

I then put down "B.C" (not possible case) which gives me a wrong answer, hence, I cannot use the second method. Could you let me know how do I make the Method 1 work please?

Two answers.

epostma — Thu, 23 Feb 2012 23:43:28 Z

@serena88: As to your first question / method, ?LinearAlgebra:-DotProduct works only on pairs of Vectors, not on Matrices. It is meant to represent the inner product on real or complex vector spaces. If the product you're trying to compute involves Matrices, use . (the dot), as you found already, or ?LinearAlgebra:-Multiply (which does the same thing, I think).

As to your second question: actually, B . C is well defined: B is a 3x1 Matrix and C a 1x2 Matrix, so you can multiply them to obtain a 3x2 Matrix (since nxk and kxm matrices can be multiplied for any n, k, m to obtain nxm matrices). If you would use, say, C^+ (a 2x1 Matrix) instead of C, then Maple would complain.

Hope this helps,

Erik Postma
Maplesoft.