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If the determinant of is zero, it is impossible for it to have a one-sided inverse ; therefore a left inverse or right inverse implies the existence of the other one.
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If and determinant
If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of A is not zero.
If the Jacobian g has a non-zero determinant, then is " conformal in the generalized sense " with respect to one of the three angle types, depending on the real matrix expressed by the Jacobian g.
If we write F < sup >×</ sup > for the multiplicative group of F ( excluding 0 ), then the determinant is a group homomorphism
If Q is not degenerate, we can see what type of conic section it is by computing the minor ( that is, the determinant of the submatrix resulting from removing the last row and the last column of A < sub > Q </ sub >):
If V is finite-dimensional then its dimension must necessarily be even since every skew-symmetric matrix of odd size has determinant zero.
* If G is SL ( 2, R ) ( real 2 × 2 matrices with determinant 1 ), the Lie algebra of G consists of real 2 × 2 matrices with trace 0.
For n functions of several variables, a generalized Wronskian is the determinant of an n by n matrix with entries D < sub > i </ sub >( f < sub > j </ sub >) ( with 0 ≤ i < n ), where each D < sub > i </ sub > is some constant coefficient linear partial differential operator of order i. If the functions are linearly dependent then all generalized Wronskians vanish.
If this determinant is zero then x is called a degenerate critical point of f, this is also called a non-Morse critical point of f. Otherwise it is non-degenerate, this is called a Morse critical point of f.
If B is a skew symmetric matrix, then its determinant is equal to its Pfaffian squared:
If complex numbers are realized as 2 × 2 real matrices ( see complex number ), the unit complex numbers correspond to 2 × 2 orthogonal matrices with unit determinant.
* If the economy follows adaptive expectations, future inflation is partly determined by past experience with inflation, since experience determines expected inflation and this is a major determinant of realized inflation.
If V is finite-dimensional then, relative to some basis for V, a bilinear form is degenerate if and only if the determinant of the associated matrix is zero – if and only if the matrix is singular, and accordingly degenerate forms are also called singular forms.
If the determinant is 0, or has common factors with the modular base, then the matrix cannot be used in the Hill cipher, and another matrix must be chosen ( otherwise it will not be possible to decrypt ).
If A is a square matrix, then the minor of its entry, also known as the i, j, or ( i, j ), or ( i, j )< sup > th </ sup > minor of A, is denoted by and is defined to be the determinant of the submatrix obtained by removing from A its i-th row and j-th column.
If is a rank-two tensor density of weight W with covariant indices then the matrix determinant will have weight, where N is the number of space-time dimensions.
If only one spin orbital differs, we describe this as a single excitation determinant.
If two spin orbitals differ it is a double excitation determinant and so on.
If the circles are represented in trilinear coordinates in the usual way, then their radical center is conveniently given as a certain determinant.
If both players ' optimal strategies are mixed strategies then the outcome of the game cannot be certainly determinant ( as it can for pure strategies, since these are deterministic ).
If all quantities converge in an appropriate sense, then the functional determinant can be described as a classical limit ( Watson and Whittaker ).
If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If and zero
If the polarities are correct, the platform rotates in such a direction as to reduce the accelerometer output to zero.
If the polarity is correct, the platform will turn until the heading error angle is zero.
If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero.
If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.
If all four players pass in the first round, the deal is not played ; in rubber bridge the deal is not scored and the hand is redealt by the original dealer, while in duplicate the score is recorded as zero for each pair and returned to the board.
If the remaining array to be searched is reduced to zero, then the key cannot be found in the array and a special " Not found " indication is returned.
If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).
If they are successful, they receive two points, if they are not, then they receive zero points.
If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).
If the desired user's code has nothing in common with the signal the correlation should be as close to zero as possible ( thus eliminating the signal ); this is referred to as cross correlation.
If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible.
If the dot product is zero, the two vectors are said to be orthogonal to each other.
If h is negative, then a + h is on the low part of the step, so the secant line from a to a + h is very steep, and as h tends to zero the slope tends to infinity.
If h is positive, then a + h is on the high part of the step, so the secant line from a to a + h has slope zero.
If a vector field F with zero divergence is defined on a ball in R < sup > 3 </ sup >, then there exists some vector field G on the ball with F = curl ( G ).
If the remainder is zero the answer produced is ' yes ', otherwise it is ' no '.
If they fail to perform the dive announced, even if they physically cannot execute the dive announced or if they perform a more difficult dive, they will receive a score of zero.
If a dive is performed which is as submitted but not as ( incorrectly ) announced, it is declared failed and scores zero according to a strict reading of the FINA law.
If an explosive molecule contains just enough oxygen to convert all of its carbon to carbon dioxide, all of its hydrogen to water, and all of its metal to metal oxide with no excess, the molecule is said to have a zero oxygen balance.
If the moments of the aligned and anti-aligned ions balance completely so as to have zero net magnetization, despite the magnetic ordering, then it is an antiferromagnet.
If the arguments are both greater than zero then the algorithm can be written in more elementary terms as follows:
If a and b are not both zero, the greatest common divisor of a and b can be computed by using least common multiple ( lcm ) of a and b:
If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames, because straight-line motion can be observed in a variety of frames.
0.354 seconds.