In linear algebra, a row vector is a 1 × n matrix, that is, a matrix consisting of a single row: Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), linear transformations, and systems of linear equations in finite dimensions. ... In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a ring-like algebraic structure. ...

The transpose of a row vector is a column vector. In mathematics, and in particular linear algebra, the transpose of a matrix is another matrix, produced by turning rows into columns and vice versa. ... In linear algebra, a column vector is an m × 1 matrix, i. ...

The set of all row vectors forms a vector space which is the dual space to the set of all column vectors. A vector space (or linear space) is the basic object of study in the branch of mathematics called linear algebra. ... In mathematics, the existence of a dual vector space reflects in an abstract way the relationship between row vectors (1×n) and column vectors (n×1). ... In linear algebra, a column vector is an m × 1 matrix, i. ...

Notation

To simplify writing column vectors in-line with other text, sometimes they are written as row vectors with the transpose operation applied to them. In linear algebra, a column vector is an m × 1 matrix, i. ... In mathematics, and in particular linear algebra, the transpose of a matrix is another matrix, produced by turning rows into columns and vice versa. ...

For further simplification, writers also use the convention of writing both column vectors and row vectors as rows but separating row vector elements with spaces and column vector elements with commas. For example, if x is a row vector, then x and x^T might be denoted as follows. In linear algebra, a column vector is an m × 1 matrix, i. ... A space is a punctuation convention for providing interword separation in some scripts, including the Latin, Greek, Cyrillic, and Arabic. ... In linear algebra, a column vector is an m × 1 matrix, i. ... A comma ( , ) is a punctuation mark. ...

Operations

• Matrix multiplication involves the action of multiplying each column vector of one matrix by each row vector of another matrix.

• The dot product in a Euclidean space involves both taking the transpose of a column vector and multiplying the resulting row vector with another column vector.