1×K

1×k may refer to either a simple arithmetic product or to a matrix shape. The arithmetic interpretation is straightforward: for any numbers or matrices, 1 × k equals k, since multiplying by one leaves the other factor unchanged.

In linear algebra, 1×k denotes a matrix with one row and k columns—a row vector of length k. A typical representation is a1, a2, ..., ak. The transpose of a 1×k matrix is a k×1 column vector. If v is a 1×k row vector and w is a k×1 column vector, their product v w is a 1×1 matrix, equal to the dot product sum ai wi. Row vectors are used to express linear functionals on R^k, to represent features in data sets, and as the first operand in matrix multiplications that yield scalar projections.

When used to describe data shapes, 1×k emphasizes the arrangement of elements in a single row. It contrasts with k×1, which denotes a column vector. The two are transposes of each other. In programming and data analysis, 1×k arrays correspond to single samples with k attributes; 1×k matrices can be stacked to form larger matrices.

Example: with k=3, the row vector [1, 0, -2] times the column vector [x, y, z]^T yields x − 2z. In summary, 1×k is a compact way to specify either a scalar product or a one-row, k-column matrix, depending on context.