CODEWITHSUNDEEP
pandasnumpymathnumpy-ndarray
NewDev
NewDev

Reputation: 61

Vectors vs ndarrays in pandas/numpy

I know for a 4D vector, shape should be (4, 1) which is actually represented in 4D space but ndim is 2, and for some ndarray to be in 4 dimension, its shape should be something like (2, 3, 4, 5).

So, Is it like dimensional concept differs between vector and matrices (or arrays)? I'm trying to understand from mathematical perspective and how it's derived to pandas programming.

Upvotes: 1

Views: 190

Answers (1)

amzon-ex
amzon-ex

Reputation: 1744

The dimensionality of a mathematical object is usually determined by the number of independent parameters in that particular object. For example, a 4-D vector is mathematically 4 dimensional because it contains 4 independent elements (unless some relation between them has been specified). Such a vector, if represented as a column vector in numpy, would have a shape (4, 1) because it has 4 rows and 1 column. The transpose of this vector, a row vector, has shape (4, ) because it has 4 columns and only 1 row, and the row-style view is default, so if there is 1 row, it's not explicitly mentioned.
Note however, that the column vector and row vector are dimensionally equivalent mathematically. Both have 4 dimensions. For a 3 x 3 matrix, the most general mathematical dimension is 9, because it has 9 independent elements in general. The shape of a corresponding numpy array would be (3, 3). If you're looking for the maximum number of elements in any numpy array, ndarray.size is the way to go.

ndarray.ndim, however, yields the number of axes in a numpy array. That is, the number of directions along which values are placed (sloppy terminology!). So for the 3 x 3 matrix, ndim yields 2. For an array of shape (3, 7, 2, 1), ndim would yield 4. But, as we already discussed, the mathematical dimension would generally be 3 x 7 x 2 x 1 = 42 (So this is a matrix in 42-dimensional space! But the numpy array has just 4 dimensions). Thereby, as you might've already noticed, ndarray.size is just the product of the numbers in ndarray.shape.

Note that these are not just concepts of programming. We are used to saying "2-D matrices" in mathematics, but that is not to be confused with the space in which the matrices reside.

Upvotes: 1

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