mathbfx2

"mathbfx2" is a mathematical notation used to represent the square of a vector or matrix. It is commonly employed in linear algebra and related fields to denote the operation of multiplying a vector or matrix by itself. This notation is particularly useful in the context of quadratic forms, where the square of a vector is involved.

In the context of vectors, "mathbfx2" typically refers to the dot product of a vector with itself. For a vector "mathbfx" in n-dimensional space, "mathbfx2" is calculated as the sum of the squares of its components. Mathematically, this can be expressed as:

"mathbfx2" = "mathbfx" · "mathbfx" = "x12" + "x22" + ... + "xn2"

where "x1", "x2", ..., "xn" are the components of the vector "mathbfx".

In the context of matrices, "mathbfx2" can refer to the matrix product of a matrix "mathbfx" with itself. This operation is defined only when the matrix is square (i.e., it has the same number of rows and columns). The resulting matrix is also square and has the same dimensions as the original matrix.

The notation "mathbfx2" is concise and avoids the need for more verbose expressions like "mathbfx" squared or "mathbfx" transposed times "mathbfx". It is widely used in mathematical literature and software implementations to represent these operations succinctly.