Re: How to transpose vector?
- To: mathgroup at smc.vnet.net
- Subject: [mg14673] Re: How to transpose vector?
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Sun, 8 Nov 1998 21:15:33 -0500
- References: <720th6$1vl@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Nobuhiko Tamura wrote in message <720th6$1vl at smc.vnet.net>...
>I have a problem about manupirating vectors. I wanted to make 3x3
>matrixtwo by using 3x1 vector alpha and beta. and I tried by
>
>>>Transpose[alpha].beta
>
>but it dosen't work.
>Please tell me how to do it.
>
>Sorry for poor English.
>Nobuhiko Tamura
>@Chiba university
>Japan
>
>Email-> ntamura at tky2.3web.ne.jp
>
Nabuhiko,
It looks as if you want to use, what traditionally would be written
(leaving out brackets)
like
a1 . (b1,b2,b3) = a1 b1, a1 b2, a1 b3 a2 a2
b1, a2 b2, a2 b3 a3 a3 b1, a3 b2, a3 b3
To get the same result with Mathematica we need
{{a1}, {a2}, {a3}}. {{b1, b2, b3}}
{{a1 b1, a1 b2, a1 b3}, {a2 b1, a2 b2, a2 b3}, {a3 b1, a3 b2, a3 b3}}
or
Transpose[{{a1, a2, a3}}].{{b1, b2, b3}}
{{a1 b1, a1 b2, a1 b3}, {a2 b1, a2 b2, a2 b3}, {a3 b1, a3 b2, a3 b3}}
*** In Mathematica a vector is simply a list like {a1,a2,a3} (and this
cannot be transposed)***.
To change it to a matrix form we can use
List[{a1, a2, a3}]
{{a1, a2, a3}}
giving a 1 by 3 matrix
or
List/@{a1, a2, a3}
{{a1}, {a2}, {a3}}
giving a 3 by 1 matrix
*** However, there is a way of getting the answer that you want directly
from vectors***:
Outer[Times, alpha, beta]
{{a1 b1, a1 b2, a1 b3}, {a2 b1, a2 b2, a2 b3}, {a3 b1, a3 b2, a3 b3}}
Allan,
---------------------
Allan Hayes
Mathematica Training and Consulting
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
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