Let Q 1 and Q 2 be n × n nonzero quadratic matrices and let c 1 and c 2 be nonzero complex numbers. Necessary and sufficient conditions for the quadraticity of the linear combinations of the form Q = c 1 Q 1 + c 2 Q 2 are obtained. Our main results contain many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices. Finally, some numerical examples are given to exemplify the main results.
Digital systems consist of thousands of digital circuit blocks operating in the background, working in their simplest form such as addition, subtraction, multiplication, division. In exponential expressions like square roots and cube roots, just like these circuits, it is found in many digital systems and performs tasks. Although these processes seem to be used only in circuits carrying out mathematical operations, they actually take an active role in solving many engineering problems. In this study, a digital circuit design that computes both the integer and a floating point exponent of a 32-bit floating-point number has been realized. This digital circuit, which is coded with VHDL language, can be used from beginner to advanced level in FPGA based systems. This digital circuit, which is coded with VHDL language, can be used from beginner to advanced level in FPGA based systems. In addition, three floating IP cores - logarithm, multiplication and exponent - were used in this digital circuit, and results were obtained with a total of five finite state machines in sixty-six clock pulse time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.