If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the Hessian is positive definite at x, then f attains a local minimum at x.

If the Hessian is negative definite at x, then f attains a local maximum at x.

If the Hessian has both positive and negative eigenvalues then x is a saddle point for f ( this is true even if x is degenerate ).

If is a point over the Hessian curve with parameter d =

If there are proteins left in the shell matrix, it is also possible that they can trigger an allergic ( asthmatic ) attack.

If A is expressed as an N × N matrix, then A < sup >†</ sup > is its conjugate transpose.

If matrix support is polar ( e. g. paper, silica etc.

If the condition number is close to one, the matrix is well conditioned which means its inverse can be computed with good accuracy.

If the condition number is large, then the matrix is said to be ill-conditioned.

If we write an n-by-n matrix in terms of its column vectors

If the matrix entries are real numbers, the matrix can be used to represent two linear mappings: one that maps the standard basis vectors to the rows of, and one that maps them to the columns of.

If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices.

If is a quaternion valued spinor, is quaternion hermitian 4x4 matrix coming from Sp ( 8 ) and is a pure imaginary quaternion ( both of which are 4-vector bosons ) then the interaction term is:

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

If he used the punch and matrix approach, all his letters should have been nearly identical, with some variations due to miscasting and inking.

If G is any subgroup of GL < sub > n </ sub >( R ), then the exponential map takes the Lie algebra of G into G, so we have an exponential map for all matrix groups.

* If the message indicates, Bob would send his qubit through the unitary gate given by the Pauli matrix

If one considers the matrix A as a linear mapping

* If A is a square matrix ( i. e., m = n ), then A is invertible if and only if A has rank n ( that is, A has full rank ).

* If B is any n-by-k matrix, then

* If B is an n-by-k matrix with rank n, then

* If C is an l-by-m matrix with rank m, then

* Sylvester ’ s rank inequality: If A is a m-by-n matrix and B n-by-k, then

If the impression is made purely as a relief resulting from the greater pressure on the paper where the high parts of the matrix touch, the seal is known as a dry seal ; in all other cases a liquid or liquified medium ( such as ink or wax ) is used, usually in another color than the paper.

If A is a matrix,

If the matrix is positive semidefinite matrix, then is a convex function: In this case the quadratic program has a global minimizer if there exists some feasible vector ( satisfying the constraints ) and if is bounded below on the feasible region.

If the matrix is positive definite and the problem has a feasible solution, then the global minimizer is unique.

If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??

If you tell him I made a pass at you he might think you misunderstood something I said or did, so instead of just telling him I made a pass, say I tried to date you and that you agreed so you could prove to him what a louse I really am.

If we look at recent art we find it preoccupied with form.

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If living Jews were unavailable for study, the Bible was at hand.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If it proclaims that the best is yet to be, it always arouses, at least in the young, either a suspicious question or perhaps the exclamation of the Negro youth who saw on a tombstone the inscription, `` I am not dead but sleeping ''.

If a broader Atlantic community is to be formed -- and my own judgment is that it lies within the realm of both our needs and our capacity -- a ready nucleus of machinery is at hand in the NATO alliance.

If you're lyin' out in the hammock at night, and it gets kinda cool -- you know -- you just take these sides with the fringe on -- see -- and wrap 'em right over you.

Mr. Richard Preston, executive director of the New Hampshire State Planning and Development Commission, in his remarks to the Governors Conference on Industrial Development at Providence on October 8, 1960, warned against the fallacy of attempting to attract industry solely to reduce the tax rate or to underwrite municipal services such as schools when he said: `` If this is the fundamental reason for a community's interest or if this is the basic approach, success if any will be difficult to obtain ''.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.

If Joe doesn't show up, we'll all be back here at 0600 hours.

If he had any worries, it was only the small ones, about Mother in New York, and his daughter Edwina and what she might be doing at this hour, with her Aunt Asia, in Philadelphia.

`` If William agrees, we should insist on a public debate '', he said at length.

If we sit here reading editorials and looking at public-opinion polls and other reports that cross our desks, we should realize that this is raw, undigested opinion expressed in the absence of leadership.

If our national interest lies in being able to fight and win a war rather than committing national suicide, then we must take a much more penetrating look at ballistic missiles.

If our SAC bombers were, today, capable of surviving a surprise missile attack and because of infinite dispersion or long endurance had the capability to strike at Russia again, and again, and again, those bombers would unquestionably assure our military dominance.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

If the lever is pulled to clear a signal or move a switch, the tappet moves a short distance lengthwise at the same time.

If the background of design is too smooth, or you wish to create a wood-grained effect, it may be added at this time with a dull tool such as the handle of a fine paintbrush.