# [Numpy-discussion] Some comments on the Numeric3 Draft of 1-Mar-05

Bruce Southey southey at uiuc.edu
Wed Mar 2 12:15:24 CST 2005

```Hi,

>>>  I suggest that Numeric3 offers the opportunity to drop the word rank
>>> from its lexicon.  "rank" has an established usage long before
>>> digital computers.  See: http://mathworld.wolfram.com/Rank.html
>>
>>
>> The meaning of "tensor rank" comes very close and was probably the
>> inspiration for the use of this terminology in array system.
>
>Yes: The total number of contravariant
><http://mathworld.wolfram.com/ContravariantTensor.html> and covariant
><http://mathworld.wolfram.com/CovariantTensor.html> indices of a tensor
><http://mathworld.wolfram.com/Tensor.html>. The rank of a tensor
><http://mathworld.wolfram.com/Tensor.html> is independent of the number
>of dimensions <http://mathworld.wolfram.com/Dimension.html> of the space
><http://mathworld.wolfram.com/Space.html>.
>
>I was thinking in terms of linear independence, as with Matrix Rank: The
>rank of a matrix <http://mathworld.wolfram.com/Matrix.html> or a linear
>map <http://mathworld.wolfram.com/LinearMap.html> is the dimension
><http://mathworld.wolfram.com/Dimension.html> of the range
><http://mathworld.wolfram.com/Range.html> of the matrix
><http://mathworld.wolfram.com/Matrix.html> or the linear map
><http://mathworld.wolfram.com/LinearMap.html>, corresponding to the
>number of linearly independent
><http://mathworld.wolfram.com/LinearlyIndependent.html> rows or columns
>of the matrix, or to the number of nonzero singular values
><http://mathworld.wolfram.com/SingularValue.html> of the map.
>
>I guess there has been a tussle between the tensor users and the matrix
>users for some time.
>

If you come from the linear algebra, rank is the column or row space which is
not the current usage in numarray but this is the Matlab usage. The matrix rank
doesn't exist in numarray (as such, but can be computed) so the only problem
for is remembering what rank provides and avoiding it in numarray.

>>
>>>  Perhaps some abbreviation for "Dimensions" would be acceptable.
>>
>>
>> The equivalent of "rank" is "number of dimensions", which is a bit
>> long for my taste.
>
>Perhaps nDim, numDim or dim would be acceptable.
>

There needs to be a clarification that by dimensions, one does not mean the
number of rows and columns etc. However, taking directly from the numarray
manual:
"The rank of an array A is always equal to len(A.getshape())."

So I would guess the best solution is to find out how people actually use the
term 'rank' in Numerical Python applications.

Regards
Bruce

```