Recent content by lolittaFarhat

##\frac{dH}{dx}## and ##\frac{dH}{dy}## in V are continuous, how can this help?

Let H be a real-valued function of two real variables with continuous first partial derivatives. If h(z)=h(x+i y)= u(x,y)+iv(x,y)is holomorphic in a region V, and H(u,v)=0. Find a condition on H under which one can conclude that h is a constant . Of, course H is the zero function can do the job...

z1,z2,z3 are distinct complex numbers, prove that they are the vertices of an equilateral triangle if and only if the following relation is satisfied: z1^2+z2^2+z3^2=z1.z2+z2.z3+z3.z1 so i shall show that |z1-z2|=|z1-z3|=|z2-z3|but i do not know how to start.

A is an nxn matrix, I is its identity and should be also an nxn matrix, k must be equal to n because we want A-xrI . Here is the exact statement of the problem: Let A ∈Rnxn, x ∈ Rk. Find the first column of M = (A − x1I)(A − x2I)...(A − xkI) using a sequence of GAXPY’s operations.

what you thought is absolutely right, A is a matrix in R^(nxn) and x is an element of R^K . r is a real variable that is equal to k. Sorry for misstating the problem statement.

Homework Statement Let A be an nxn matrix belonging to R and x be a vector of length k belonging to R. Find the first column of M = (A − x1I)(A − x2I)...(A − xrI) using a sequence of GAXPY’s operations. Homework Equations GAXPY: General matrix A multiplied by a vector X plus a vector Y The...

Homework Statement Show that the only m for which the subspace of C given by {z ∈ C: Im(z) = m Re(z)} is a field is m=0. Homework Equations Field axioms The Attempt at a Solution I tried to prove one direction : - If z is in the subspace, Re z>0 and m≠0 then Arg z<Arg z^2, so z^2 is not in...