Kx1xn

kx1xn is a shorthand notation used to describe a three-dimensional array with dimensions k, 1, and n. The symbol is commonly encountered in discussions of linear algebra, numerical computing, and machine learning. Here k and n denote positive integers; the middle dimension has size one, making it a singleton dimension. The total number of elements is k × 1 × n = k·n.

Characteristics include the presence of a singleton dimension, which does not carry additional data but affects how operations are applied across axes. In programming languages and libraries that support broadcasting, a tensor with shape (k, 1, n) can be combined with tensors of compatible shapes by expanding the size of the singleton dimension to match the corresponding axis of the other tensor.

Examples help illustrate this. A tensor with shape (3, 1, 4) and another with shape (3, 5, 4) can participate in elementwise operations by broadcasting the (3, 1, 4) tensor to (3, 5, 4). For matrix multiplication, the singleton dimension is typically collapsed or addressed through reshaping, since standard matrix products expect compatible inner dimensions. In neural networks and data processing, shapes like (batch, 1, sequence_length) or (k, 1, n) commonly appear when applying the same operation across multiple sequences or features.

Related concepts include tensor shape notation, broadcasting rules, three-dimensional arrays, and reshaping. Understanding kx1xn helps in reasoning about memory layout, broadcasting behavior, and dimensionality in multi-dimensional data.