N-dimensional vectors and matrices are both used in linear algebra to represent sets of numbers. However, there is a fundamental difference between the two.

A vector is a one-dimensional array of numbers, which can be represented as a list or an array in Python. Each element in the list corresponds to a value in the vector. For example, a 3-dimensional vector can be represented as [x, y, z], where x, y, and z are the values of the vector in each dimension.

On the other hand, a matrix is a two-dimensional array of numbers, which can also be represented as a list of lists or an array in Python. Each element in the matrix corresponds to a value in a specific row and column. For example, a 2x3 matrix can be represented as [[a, b, c], [d, e, f]], where a, b, c, d, e, and f are the values in the matrix.

In summary, while both vectors and matrices represent sets of numbers, vectors are one-dimensional while matrices are two-dimensional.
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