Why are isscalar, isvector and ismatrix all true for A = 1?

Question

Matlab has the following functions to check inputs:

• isscalar to determine whether input is scalar
• isvector to determine whether input is a vector
• ismatrix to determine whether input is a matrix

For A = 1 (or any "scalar" input) all of the above return true.
Why do I see this counter-intuitive behavior?
And how would I indentify A = 1 as scalar?

Answer 1

I don't find it counter-intuitive at all. In Mathematics there exist vectors of 1 dimension (even though they are isomorphic with scalars). Also, a matrix can perfectly have size 1x1.

It is true that a single number could be considered a scalar, a 1-vector or a 1x1 matrix. Matlab's view is:

• A scalar is considered to be a 1x1 matrix
• An n-vector is just a 1 x n or n x 1 matrix

• More generally: trailing singleton dimensions don't count. For example, a 3D-array of size 2x3x4 can also be considered, say, a 5D-array of size 2x3x4x1x1. This works without error:

  >> a = rand(2,3,4);
  >> a(2,2,2)
  ans =
      0.2575
  >> a(2,2,2,1,1)
  ans =
      0.2575
  

Now, if you want to check if A is a vector, matrix, or multidimensional array with more than one element, use

numel(A)>1

The numel function returns the number of elements of its input argument.

Answer 2

Because Matlab interprets scalars as 1-by-1 arrays, see the size documentation.

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Therefore, depending on your application, you would have to

• use isscalar to distinguish a vector from a scalar (because it will return false for a vector)
• use isvector to distinguish a matrix from a vector (because it will return false for a matrix)

Because if you are trying to figure out if a variable is a vector and not a scalar and you use isvector, both a scalar and a vector will return true - as pointed out in the question.