Sentence examples for regular pencil from inspiring English sources

In this section, we consider the case of the system (1) with a regular pencil.

Theorem 2.1 Consider the system (1) with a regular pencil and boundary conditions of type (2).

Where sF w - Q w is the complex Weierstrass form of the regular pencil sF-G and is defined by s F w - Q w : = s I p - J p ⊕ s H q - I q (7).

where Q p ∈ M m p is a matrix with columns p linear independent (generalized) eigenvectors of the p finite eigenvalues of s F − G, and Q q ∈ M m q is a matrix with columns q linear independent (generalized) eigenvectors of the q infinite eigenvalues of s F − G. Lemma 2.1 Consider the system (1) with a regular pencil.

The complex Weierstrass form s F w − Q w of the regular pencil s F − G is defined by s F w − Q w : = s I p − J p ⊕ s H q − I q, where the first normal Jordan-type element is uniquely defined by the set of the finite eigenvalues of s F − G and has the form s I p − J p : = s I p 1 − J p 1 ( a 1 ) ⊕ … ⊕ s I p ν − J p ν ( a ν ).

Then, the complex Weierstrass form sF w - Q w of the regular pencil sF - G is defined by sF w - Q w := sI p - J p ⊕ sH q - I q, where the first normal Jordan-type element is uniquely defined by the set of f.e.d. ( s - a 1 ) p 1,..., ( s - a ν ) p ν, ∑ j = 1 ν p j = p (6). of sF - G and has the form s I p - J p : = s I p 1 - J p 1 ( a 1 ) ⊕ ⋯ ⊕ s I p ν - J p ν ( a ν ).

"I never knew those kind of supplies existed," said Anclaudys, who had used only regular pencils up to that point.

I gave up on regular pencils after the Blackwings (none were satisfactory) but I have become very attached to the more delicate lines of the Pentel mechanical pencil.

At G.M., that means stocking offices with regular pencils instead of mechanical ones, holding dealer meetings on the phone rather than in person, and canceling sponsorships of charity golf tournaments and high-profile events like the Academy Awards.

Thus, in our approach, using the Thompson canonical form for regular pencils, necessary and sufficient conditions for the solvability of a general class of such systems are obtained.

and the minimal indices (m.i .. Unlike the case of the regular pencils, where the pencil is characterized only from the e.d., the characterization of a singular matrix pencil apart from the set of the determinantal divisors requires the definition of additional sets of invariants, the minimal indices.