N×B

N×B denotes the dimensions of a rectangular array, typically a matrix or data table, with N rows and B columns. The size is read as “N by B.” The first dimension is usually associated with observations or samples, while the second corresponds to features, attributes, or variables. In many contexts, an N×B data matrix X represents N samples each described by B features.

In linear algebra, the transpose of an N×B matrix X has size B×N. If A is N×B and C is B×M, the product AC exists and has size N×M; the inner dimension B must match. For example, a 3×4 matrix multiplied by a 4×2 matrix yields a 3×2 result.

The rank of an N×B matrix is at most min(N,B). If the matrix has full row rank (rank equal to N), then N ≤ B and the N rows are linearly independent. If it has full column rank (rank equal to B), then B ≤ N and the B columns are independent. Non-square matrices do not have determinants, but many properties relate to rank, such as solvability of linear systems and the existence of inverse-like pseudoinverses.

In data applications, N×B is commonly used to describe a dataset with N observations and B features, but conventions vary by field. The notion also appears when forming weight matrices in algorithms, transforming data via multiplication, or reshaping arrays for computational pipelines. Overall, N×B provides a concise way to specify the shape constraints that govern matrix operations and data organization.