Matrix Multiplication
- To: mathgroup@smc.vnet.net
- Subject: [mg12259] Matrix Multiplication
- From: Des Penny <dpenny@iname.com>
- Date: Tue, 5 May 1998 03:29:55 -0400
Hi Folks:
I ran into the following little problem that has me puzzled.
I'm trying to multiply a 3x1 matrix and a 1x2 matrix. I should get a
3x2 matrix, but instead I get an error message:
In: A=Array[a,{3,1}]
Out: {{a[1,1]},{a[2,1]},{a[3,1]}}
In: B=Array[b,{2}]
Out: {b[1],b[2]}
In: A.B
Dot::"dotsh": "Tensors \!\({\({a[\(1, 1\)]}\), \({a[\(2, 1\)]}\),
\({a[\(3, 1\)]}\)}\) and \!\({\(b[1]\), \(b[2]\)}\) have incompatible
shapes."
Out: {{a[1,1]},{a[2,1]},{a[3,1]}}.{b[1],b[2]}
Of course I can get what I want by:
In: A1=Flatten[A]
Out: {a[1,1],a[2,1],a[3,1]}
In: Outer[Times, A1, B]
Out: {{a[1,1] b[1],a[1,1] b[2]},{a[2,1] b[1],a[2,1] b[2]},{a[3,1]
b[1],a[3,1] b[2]}}
I don't seem to have trouble with any other dimensions e.g.
In: A=Array[a,{3,2}]
Out: {{a[1,1],a[1,2]},{a[2,1],a[2,2]},{a[3,1],a[3,2]}}
In: B=Array[b,{2,4}]
Out: {{b[1,1],b[1,2],b[1,3],b[1,4]},{b[2,1],b[2,2],b[2,3],b[2,4]}}
In: A.B
Out: {{a[1,1] b[1,1]+a[1,2] b[2,1],a[1,1] b[1,2]+a[1,2] b[2,2],a[1,1]
b[1,3]+a[1,2] b[2,3],a[1,1] b[1,4]+a[1,2] b[2,4]},{a[2,1] b[1,1]+a[2,2]
b[2,1],a[2,1] b[1,2]+a[2,2] b[2,2],a[2,1] b[1,3]+a[2,2] b[2,3],a[2,1]
b[1,4]+a[2,2] b[2,4]},{a[3,1] b[1,1]+a[3,2] b[2,1],a[3,1] b[1,2]+a[3,2]
b[2,2],a[3,1] b[1,3]+a[3,2] b[2,3],a[3,1] b[1,4]+a[3,2] b[2,4]}}
Can anyone explain what's going on?
Thanks for your help.
Cheers,
Des Penny
penny@suu.edu