C1X1

c1x1 (sometimes written as C1X1) is a notation that appears in several technical contexts and is most commonly associated with linear algebra and deep‑learning convolutional operations. In linear algebra, a c1x1 matrix denotes the trivial case of a square matrix with only one row and one column. Because it contains a single element, all matrix operations on a c1x1 reduce to operations on a scalar. This form is often used for clarity or to emphasize the dimensionality of a matrix in proofs or algorithmic descriptions.

In computer vision and neural‑network design, a c1x1 refers to a one‑by‑one convolution filter, also known as a point‑wise convolution. Applied over an input feature map, a 1×1 kernel transforms the channel dimension without changing the spatial resolution. By combining several c1x1 layers with larger spatial filters, network architects can effectively construct depth‑wise separable convolutions that reduce the number of parameters and computational cost. The use of c1x1 layers became popular in architecture families such as Inception, MobileNet, and others that prioritize efficiency.

The term also occasionally appears in hardware design literature to describe a single‑element crossbar or a 1×1 memory block, especially when discussing scaling or layout considerations in integrated circuits.

Because the notation is concise, it is frequently encountered in research papers, textbooks, and industry documentation that involve small matrix operations or lightweight convolutional layers. Mastery of the c1x1 concept is useful for mathematics students examining matrix theory as well as for engineers designing efficient neural‑network models.