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Scalars, Vectors and Matrices

Mathematica represents matrices and vectors using lists. Anything that is not a list Mathematica considers as a scalar.
A vector in Mathematica consists of a list of scalars. A matrix consists of a list of vectors, representing each of its rows. In order to be a valid matrix, all the rows must be the same length, so that the elements of the matrix effectively form a rectangular array.
VectorQ[expr]give True if expr has the form of a vector, and False otherwise
MatrixQ[expr]give True if expr has the form of a matrix, and False otherwise
Dimensions[expr]a list of the dimensions of a vector or matrix

Functions for testing the structure of vectors and matrices.

The list {a, b, c} has the form of a vector.
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Anything that is not manifestly a list is treated as a scalar, so applying VectorQ gives False.
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This is a 23 matrix.
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For a vector, Dimensions gives a list with a single element equal to the result from Length.
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This object does not count as a matrix because its rows are of different lengths.
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