Fixedmatrices

Fixedmatrices are a concept in abstract algebra, specifically within the study of matrices. A fixedmatrix is a matrix whose entries are fixed, meaning they are constants and do not vary. This distinguishes them from matrices whose entries can be parameters or functions. In many contexts, matrices are assumed to be fixed unless otherwise specified. For example, when discussing a linear transformation represented by a matrix, the entries of that matrix are typically considered to be fixed values that define the specific transformation.

The term "fixedmatrix" is not a standard or widely recognized term in formal mathematical literature. Instead, mathematicians typically refer to matrices with constant entries simply as "matrices" or "constant matrices" when the distinction from variable matrices is important. The concept arises implicitly when one needs to differentiate between matrices that are part of a computation with unchanging values and those that might be part of a larger system where their values can change or are dependent on other variables. For instance, in numerical analysis, algorithms often operate on fixed matrices to solve systems of equations or perform operations. The emphasis is on the deterministic nature of the matrix's components.