Elementary matrix algebra

Elementary Linear Algebra

Elementary Microarchitecture Algebra

We describe a set of remarkably simple algebraic laws governing microarchitectural components. We apply these laws to incrementally transform a pipeline containing forwarding, branch speculation and hazard detection so that all pipeline stages and forwarding logic are removed. The resulting unpipelined machine is much closer to the reference architecture, and presumably easier to verify.

Elementary algebra revisited: Randomized algorithms

We look at some simple algorithms for elementary problems in algebra that yield dramatic efficiency improvements over standard methods through randomization. The randomized algorithms are, in a sense, “obvious”. Their formal statement was delayed partly by the need for rigorous analysis, but more so by the need to re-think traditional approaches to elementary algorithms. We illustrate this phil...

Modular Arithmetic and Elementary Algebra

where z is an integer then gcd(a, b) = gcd(b, c). Indeed any divisor of a and b will divide c, and conversely any divisor of b and c will divide a. We can compute c by taking the remainder after dividing a by b, i.e. c is a mod b. (We will discuss the mod operation in greater details in the next section, but at this point, we only need the definition of c as the remainder of dividing a by b.) B...

Notes on Elementary Linear Algebra

C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Revised August 2005 1 Vectors In quantum mechanics, we are generally interested in complex numbers. Let C denote the set of all n-tuples of complex numbers (a complex n-space). The elements of C may be called “points” or “vectors” in complex n-space. The elements of the complex numbers C are scalars. A vector...