1byn

1byN refers to a matrix with one row and N columns, equivalently a row vector of length N. In linear algebra and related fields, a 1×N object stores N features of a single observation and is often written as a row vector such as [x1, x2, ..., xN]. In software, shapes are commonly denoted as (1, N).

Transposition converts a 1×N row vector into an N×1 column vector. Matrix multiplication follows the standard rules: a 1×N matrix multiplied by an N×M matrix yields a 1×M matrix, and a 1×N matrix multiplied by an N×1 vector yields a scalar (a 1×1 matrix). The dot product of two N-dimensional vectors can be expressed as the product of a 1×N row vector and an N×1 column vector.

In data processing and machine learning, a 1×N row vector often represents a single sample with N features. Datasets are usually organized in different conventions depending on the library or framework, such as B×N (batch size by features) or N×B, but each sample can be viewed as a 1×N vector for operations like normalization, distance calculations, and feature-wise transformations.

Key distinctions exist between 1×N row vectors and N×1 column vectors. They have different orientations and are treated differently by broadcasting and memory layout in numerical computing environments. Proper handling of shapes is essential to avoid dimension mismatches during operations such as multiplication, normalization, and concatenation.

See also: row vector, column vector, dot product, matrix multiplication, transpose.