3.7.3 Scalars, Vectors and MatricesMathematica 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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VectorQ[ {a, b, c} ]
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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  matrix. | |
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Dimensions[ {{a, b, c}, {ap, bp, cp}} ]
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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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Dimensions[ {a, b, c} ]
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| This object does not count as a matrix because its rows are of different lengths. | |
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MatrixQ[ {{a, b, c}, {ap, bp}} ]
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