• Prof. Kharat Rajesh Sainath

Let a1 ........., am be such real numbers that can be expressed as a finite product of prime powers with rational exponents. Using arithmetic partial derivatives, we define the arithmetic Jacobian matrix Ja of the vector a=(a1,...., am) anologusly to the jocobian matrix Jf of a vector function f(9), we introduce the concept of multiplicative independence of {a1,..., am}and show that Ja plays in it a similar role as Jf does in functional independence. We also present a kind of arithmetic implicit function theorem and show that Ja applies to it somewhat analogously as Jf applies to the ordinary implicit function theorem.

multiplicative independence, arithmetic derivative, continuously differentiable function.

"Review Paper of Jacobian", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 1, page no.260-262, January-2019, Available :http://www.jetir.org/papers/JETIRW006057.pdf

"Review Paper of Jacobian", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 1, page no. pp260-262, January-2019, Available at : http://www.jetir.org/papers/JETIRW006057.pdf