fast Fourier transform. Abstract The broad problem of matrix algebra is taken up from the perspective of functional programming. A key question is how arrays should be represented in order to admit good implementations of well-known eecient algorithms, and whether functional architecture sheds any new light on these or other solutions. It relates directly to disarming the \ag-gregate update" pr...

The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of 1-forms is a free module over the algebra of matrices. The concept of a generalised algebra is defined and it is shown that this is required in order for the sp...

We deene an algebra on matrix pencils that is a natural extension of sums, products and quotients of real numbers. The classical algebra of linear transformations may be regarded as a special case of the algebra of pencils. The sum and product deened here preserve right deeating subspaces. We show below that the matrix sign function and the inverse-free algorithms can be derived from an algebra...

We compute the center in case q is a primitive root of unity. 1. Introduction Let F be a eld of characteristic zero. There are several ways to quantize the matrix algebra M n (F). Among them, the most common is probably the algebra introduced by Faddeev, Reshetikhin, and Takhtajan in 4]. Denote that algebra by M n (q). In 3] Dipper and Donkin deened another quantized matrix algebra which has ma...

In this paper, a series of bicomplex representation methods of quaternion division algebra is introduced. We present a new multiplication concept of quaternion matrices, a new determinant concept, a new inverse concept of quaternion matrix and a new similar matrix concept. Under the new concept system, many quaternion algebra problems can be transformed into complex algebra problems to express ...

Provenance is well-understood for relational query operators. Increasingly, however, data analytics is incorporating operations expressed through linear algebra: machine learning operations, network centrality measures, and so on. In this paper, we study provenance information for matrix data and linear algebra operations. Our core technique builds upon provenance for aggregate queries and cons...