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

Question

Matlab performs the following functions for checking inputs:

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

For A = 1 (or any "scalar" input), all of the above returns true .
Why do I see this anti-intuitive behavior?
And how would I define A = 1 as a scalar?

Answer 1

I do not find this completely intuitive. In mathematics, there are vectors of 1 dimension (although they are isomorphic to scalars). In addition, the matrix may have a size of 1x1.

It is true that one number can be considered a scalar, 1-vector or 1x1-matrix. View Matlab:

• The scalar is considered a 1x1 matrix
• An n-vector is just 1 xn or nx 1 matrix

• More generally: the long sizes of a singleton are not taken into account. For example, a 3D array of size 2x3x4 can also be considered, for example, a 5D array of size 2x3x4x1x1. This works without errors:

   >> 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 vector, matrix, or multidimensional array with more than one element , use

 numel(A)>1 

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

Answer 2

Since Matlab interprets scalars as 1-on-1 arrays see size documentation.

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Therefore, depending on your application, you should

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

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