4×1

4×1 is a notation with several meanings in mathematics and related fields. In elementary arithmetic, it denotes the product of four and one: 4×1 = 4. This simple result illustrates the multiplicative identity principle, since multiplying any number by 1 yields the original number. The expression is commutative: 4×1 = 1×4, and in general a×1 = a for any number a.

In linear algebra and matrix notation, 4×1 describes the dimensions of a matrix: a 4-by-1 matrix, i.e., a column vector with four entries. Such objects are elements of the vector space R^4 (for real components) and are typically written as a column: [v1; v2; v3; v4]. The 4×1 shape indicates four rows and one column. These vectors can participate in larger matrix operations, for example forming outer products with a 1×n row vector to yield a 4×n matrix, or serving as inputs in linear transformations and systems of equations.

Context determines interpretation. As a multiplication problem, 4×1 equals 4. As a matrix dimension, 4×1 denotes a column vector or a matrix with four rows and one column. The symbol × is used either for multiplication or to indicate dimensions, sizes, or cross products, depending on the surrounding mathematical or practical context.