Re: How to concatenate matrices?

• To: mathgroup at smc.vnet.net
• Subject: [mg113097] Re: How to concatenate matrices?
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Wed, 13 Oct 2010 12:38:49 -0400 (EDT)
• References: <201010121749.NAA03450@smc.vnet.net>

```On Oct 12, 2010, at 1:49 PM, Eduardo M. A. M.Mendes wrote:

> Hello
>
>
>
> Although I read the help on matrices, I could not figure out how to
> concatenate two matrices.
>
>
>
> What I have is:
>
>
>
> B1 - (vector) - as a result of P21.x1 (product of a matrix and a
vector)
>
> B2 - (vector) - as a result of P22.x2
>
>
>
> B=[B1,B2]  -  that is, a matrix with two columns.
>
>
>
> Join, Append, and all sort of funny functions return even funnier
results
> (elements with {}).

If x1 and x2 are 1 dimensional lists then B1 and B2 are not columns,
they are one dimensional and so do not possess columns or rows, only
length.  You can form column vectors out of B1 and B2 by giving them an
extra dimension then transposing so the length is the number of rows of
the result, eg. Transpose[{B1}].  From there you can use the
ArrayFlatten function:

ArrayFlatten[{{Transpose[{B1}],Transpose[{B2}]}}]

A shorthand for understanding all the braces in ArrayFlatten is that is
joins the rows of arrays at level 2 and the columns of arrays at level
1, so to join the rows of B1 and B2 we need to put them at level 2.

Alternatively, you can make a function that takes elements at the same
position in B1 and B2 and returns a list of those elements.  Mapping
this function over the two will result in a two column matrix:

If B1 and B2 are actual column matrices: eg. Dimensions[B1] is a list of
two values, the second of which is 1 then you can use ArrayFlatten but
omit the Transpose:

ArrayFlatten[{{B1,B2}}]

Regards,
Ssezi

```

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