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 she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

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, on the other hand, it is not settled, or while it is being debated and resolved, does the Federal government have a responsibility in situations like that in Prince Edward County??

If goodness and badness lie in attitudes only and hence are brought into being by them, those men who greeted death and misery with childishly merry laughter are taking the only sensible line.

If a union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.

If we have not thought and made a decision entirely in these terms, then we need to submit ourselves to the following `` simple test '': `` Have we decided how we are to kill the other members of our household in the event of our being less injured than they are ''??

If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.

If anything, her poems suggest the opposite – they speak of quietly experienced but intensely felt emotions, hidden from others, without any indication of being requited.

" If the aircraft is not being hijacked, the pilot should not squawk 7500 and should inform the controller accordingly.

If Acorn had thought to include this small modification in the original Electron design it is likely the machine would have had a much greater impact as it would have nearly doubled the amount of motion possible in games and saved modes 0 – 3 ( including the only 16 colour mode ) from being nearly useless due to contended memory timings.

If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.

If two equivalent amplifiers are being compared, the amplifier with higher gain settings would be more sensitive as it would take less input signal to produce a given amount of power.

If substance is the highest category and there is no substance, being, then the unity perceived in all beings by virtue of their existing must be viewed in another way.

If the first theory is correct ( see above ), then the absence of cavalry removed the main Athenian tactical disadvantage, and the threat of being outflanked made it imperative to attack.

If the slope / cliff being undercut is made of unconsolidated sediment it will erode at a much faster rate then a cliff made of bedrock.

If a cabal can be implicated in a sequence of events, there is always the hope, however tenuous, of being able to break the cabal's power – or joining it and exercising some of that power oneself.

If the experiment were done in English, since Searle knows English, he would be able to take questions and give answers without any algorithms for English questions, and he would be affectively aware of what was being said and the purposes it might serve: Searle passes the Turing test of answering the questions in both languages, but he's only conscious of what he's doing when he speaks English.

If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

If an atom A is double-bonded to an atom B, A is treated as being singly bonded to two atoms: B and a ghost atom that has the same atomic number as B but is not attached to anything except A.

If a 7 is rolled instead of the point being re-rolled, the don't pass bet wins and is paid even money.

If a demonstration of ability or knowledge is required by law before being allowed to perform a task or job, this is referred to as licensure.

If a compression test does give a low figure, and it has been determined it is not due to intake valve closure / camshaft characteristics, then one can differentiate between the cause being valve / seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby effect the mentioned seal.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

Mather began to publicize and celebrate the trials well before they were put to an end: " If in the midst of the many Dissatisfaction among us, the publication of these Trials may promote such a pious Thankfulness unto God, for Justice being so far executed among us, I shall Re-joyce that God is Glorified ..." ( Wonders of the Invisible World ).

If the business ' debts exceed its assets, the bankruptcy restructuring results in the company's owners being left with nothing ; instead, the owners ' rights and interests are ended and the company's creditors are left with ownership of the newly reorganized company.