Basic Manipulations

The transpose of a matrix a={aij} is the matrix a^t={aji}. If a is mxn, at is nxm. Let's see.

In[14]:=

  MatrixForm[a]

Out[14]=

  1    -1   1
  
  2    0    1
  
  3    -1   2

In[15]:=

  MatrixForm[Transpose[a]]

Out[15]=

  1    2    3
  
  -1   0    -1
  
  1    1    2

You can extract portions of matrices. The following give the a13 entry, the third row, and the second column of a matrix, respectively. Each row of a matrix is a row vector, each column of a matrix is a column vector.

In[16]:=

  a[[1,3]]

Out[16]=

  1

In[17]:=

  b[[1,3]]

Out[17]=

  b13

In[18]:=

  a[[3]]

Out[18]=

  {3, -1, 2}

In[19]:=

  Transpose[a] [[2]]

Out[19]=

  {-1, 0, -1}

In[20]:=

  Transpose[b] [[2]]

Out[20]=

  {b12, b22, b32, b42}

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