नॉनजीरो इसके अंग्रेजी अर्थ का उदाहरण

where a_{ij} is a nonzero positive real number if oscillator j is connected to oscillator i.

an by the same nonzero element of k gives the same point in projective space.

is an indefinite binary quadratic form with real coefficients and discriminant D b^2-4ac, then there are integers x,"nbsp;y for which f takes a nonzero value of absolute value at most.

A solvable nonzero Lie algebra has a nonzero abelian ideal, the last nonzero term in the derived series.

For each \alpha\in R^+, choose a nonzero element X_\alpha for the corresponding root space \mathfrak{g}_\alpha and a nonzero element Y_\alpha in the root space \mathfrak{g}_{-\alpha}.

Our goal is to construct a representation W_\lambda of \mathfrak{g} with highest weight \lambda that is generated by a single nonzero vector v with weight \lambda.

For each \alpha\in R^+, we choose nonzero elements X_\alpha\in\mathfrak{g}_\alpha and Y_\alpha\in\mathfrak{g}_{-\alpha}.

Indeed, the theorem says in particular that a nonzero vector spanning V_{n-1} is a common eigenvector for all the linear transformations in \pi(\mathfrak{g}).

Since \mathfrak{g} is solvable and has positive dimension, D\mathfrak{g} \ne \mathfrak{g} and so the quotient \mathfrak{g}/D\mathfrak{g} is a nonzero abelian Lie algebra, which certainly contains an ideal of codimension one and by the ideal correspondence, it corresponds to an ideal of codimension one in \mathfrak{g}.

Since the base field k is algebraically closed, there exists an eigenvector in V_{\lambda} for some (thus every) nonzero element of L.

with the center acting as a given nonzero constant.

However, the action is only defined up to multiplication by a nonzero constant, in other words, one can only map the automorphism of the group to the class [\psi]\in \operatorname{PU}(\mathcal H).