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MathGroup Archive 2000

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Re: simple questions about matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26479] Re: [mg26472] simple questions about matrices
  • From: Ken Levasseur <Kenneth_Levasseur at uml.edu>
  • Date: Thu, 28 Dec 2000 02:52:19 -0500 (EST)
  • References: <200012230346.WAA13016@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Cristian:

Here is how you perform the matrix operations.

Merry Christmas!

Ken Levasseur
Mathematical Sciences
UMass Lowell

Three credit on-line Introduction to Mathematica starts at the end of
January:  http://faculty.uml.edu/klevasseur/courses/m419/m419.html



> (a) I have a (m,n) matrix a with integer entries.How can I construct
> a separate list with the totals of adding the entries of either the
> rows or columns?
>

In[3]:=
m = Table[Random[Integer, {0, 10}], {4}, {5}]
Out[3]=
{{9, 1, 10, 4, 3}, {4, 7, 6, 9, 7}, {4, 5, 3, 3, 1}, {10, 8, 6, 4, 0}}

In[4]:=
rowsums = Apply[Plus, m, 1]
Out[4]=
{27, 33, 16, 28}
In[5]:=
columnsums = Apply[Plus, Transpose[m], 1]
Out[5]=
{27, 21, 25, 20, 11}


> (b) How can I construct a (m+1,n) matrix where the new row's entries
> are the sums of all numbers on each column?
>

In[6]:=
Append[m, columnsums]
Out[6]=
{{9, 1, 10, 4, 3}, {4, 7, 6, 9, 7}, {4, 5, 3, 3, 1},  {10, 8, 6, 4, 0},
{27, 21, 25, 20, 11}}



> (c) In general,how can I attach additional columns (o rows) to an
> existing matrix?
>
Most of the more complicated operations can be done most easily by using
the MatrixManipulation package:

In[7]:=
Needs["LinearAlgebra`MatrixManipulation`"]
In[8]:=
Information["LinearAlgebra`MatrixManipulation`*",
  LongForm -> False]
AppendColumns             MatrixNorm
AppendRows                PolarDecomposition
BlockMatrix               SquareMatrixQ
CheckLinearity            SubMatrix
HankelMatrix              TakeColumns
HilbertMatrix             TakeMatrix
InverseMatrixNorm         TakeRows
LinearEquationsToMatrices TridiagonalMatrix
LowerDiagonalMatrix       UpperDiagonalMatrix
LUMatrices                VectorNorm
MatrixConditionNumber     ZeroMatrix

Cristian Opazo-Castillo wrote:

> Hello all:
>
> I hope that someone is still working and could help me with this...
>
> (a) I have a (m,n) matrix a with integer entries. How can I construct
> a separate list with the totals of adding the entries of either the
> rows or columns?
>
> (b) How can I construct a (m+1,n) matrix where the new row's entries
> are the sums of all numbers on each column?
>
> (c) In general, how can I attach additional columns (o rows) to an
> existing matrix?
>
> Thanks a lot and Happy Holidays,
>
> Cristian



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