Similarly, SO ( n ) is a subgroup of SO ( n + 1 ); and any special orthogonal matrix can be generated by Givens plane rotations using an analogous procedure.

This can only happen if Q is an m × n matrix with n ≤ m. Similarly, QQ < sup > T </ sup > = I says that the rows of Q are orthonormal, which requires n ≥ m.

Similarly, the right multiplication of a matrix A with a scalar λ is defined to be

Similarly, each diagonal element of a skew-symmetric matrix must be zero, since each is its own negative.

Similarly, a skew-symmetric matrix is determined by n ( n − 1 )/ 2 scalars ( the number of entries above the main diagonal ).

Similarly, the absence of a normal fibronectin matrix in developing amphibians causes defects in mesodermal patterning and inhibits gastrulation.

Similarly, one can write for a 4 × 4 matrix A:

Similarly, the QR decomposition expresses A as QR with Q a unitary matrix and R an upper triangular matrix.

Similarly, a system of equations is said to be in reduced row echelon form or canonical form if its augmented matrix is in reduced row echelon form.

Similarly, defined a matrix with elements

Similarly, K < sub > 1 </ sub >( R ) is a modification of the group of units in a ring, using elementary matrix theory.

Similarly, for a rotation clockwise about the origin, the functional form is and and the matrix form is:

Similarly, the matrix values are not restricted to non-negative reals ( as they would be in the Euclidean distance matrix ) but rather can have negative values, zeros or imaginary numbers depending on the cost metric and specific use.

Similarly, the intrinsic inefficiency of the sample covariance matrix depends upon the Riemannian curvature of the space of positive-define matrices.

* Similarly, groups with property ( T ) can be used to construct finite sets of invertible matrices which can efficiently approximate any given invertible matrix, in the sense that every matrix can be approximated, to a high degree of accuracy, by a finite product of matrices in the list or their inverses, so that the number of matrices needed is proportional to the number of significant digits in the approximation.

Similarly, Japanese mathematicians were influenced by the counting rod numeral layout in their definition of the concept of a matrix.

Similarly, if Q ( n ) is the predicate " n is composite ", then

Similarly, if Q ( n ) is the predicate " n is even ", then

Similarly, if T is a subtype of U, then there is an inclusion predicate of domain type T and codomain type U that satisfies the same equation ; there are additional function symbols associated with other ways of constructing new types out of old ones.

Similarly, because meters per second, the expression f ′( g ′( 10 )) represents the change in pressure at a height of − 98 meters per second, which is also nonsense.

Similarly, we can show that the coefficient of the second term can be substituted by.

Similarly, the second syllable of the words urbem and Romam carry the metrical ictus even though the first is naturally stressed in typical pronunciation.

" The first, another word for " angry ," is " fuming ," which ends in " g ." The second, " hungry ," at least when personified, is " eager " which ends in " r ." Similarly, the third word is " every ," which ends in " y " and is clearly used by the word " everyone.

Similarly the question of whether a Turing machine T terminates on an initially empty tape ( rather than with an initial word w given as second argument in addition to a description of T, as in the full halting problem ) is still undecidable.

Similarly, Hare refers to “ the crude caricature of act utilitarianism which is the only version of it that many philosophers seem to be acquainted with .” Given what Bentham says about second order evils it would be a serious misrepresentation to say that he and similar act utilitarians would be prepared to punish an innocent person for the greater good.

Similarly if what were previously thought to be two distinct species are demoted to a lower rank, such as subspecies, where possible the second part of the binomial name is retained as the third part of the new name.

Similarly, at the 13th convocation of the CGPM in 1968, the definitive second was redefined in terms of measurements taken from atomic clocks rather than from the earth's rotation ; in 2008 the solar day was 0. 002 s longer than in 1820 but it was only in the 1960s that this could be measured more accurately using clocks rather than relying on astronomy.

" Similarly, he questioned whether the second principle means that anthropologists " approve the social caste system of India, the racial caste system of the United States, or many other varieties of social discrimination in the world ".

Similarly, Anglophones who have only one last name may be asked to provide a second last name on official documents in Spanish-speaking countries.

Similarly, in Newsweek's 2006 public high school listings Edgemont was ranked second in Westchester County and 56th nationwide.

Similarly, British industrial band Godflesh often utilized a drum machine and two primary members, although they did at times record and tour with a second guitarist ( Paul Neville of Loop ), and near the end of the band's life they began working with real drummers ( Bryan Mantia and later Ted Parsons ) almost exclusively.

Similarly, in the Belgian and UK's first season, the first words of each episode could be linked together to reveal the identity of the Mole ; in the second season, contestants were introduced in alphabetical order of their surnames, except for the Mole, who was in the correct position for " Mole ".

Similarly, students who score less than the mean on the first test will tend to see their scores increase on the second test.

Similarly, in the second diagram the naturally isomorphic spaces C, C ⊗ K and K ⊗ C are identified.

Similarly, a Cunningham chain of the second kind of length n is a sequence of prime numbers ( p < sub > 1 </ sub >,..., p < sub > n </ sub >) such that for all 1 ≤ i < n, p < sub > i + 1 </ sub >

Similarly, uttering the second line of the mantra offer other part of the rice grains to the fire after saying ' Prājapataye svāhā ' and complete the mantra uttering ' Prajāpataye idam, na mama '.

Similarly, Canada ( where Canadian football, a related sport, has widespread popularity ) did not field a team until the 2011 competition, where the Canadian team finished second to the United States.

Similarly for the second integral, we would introduce a " constant " function of x, because we have integrated with respect to y.

Similarly, the Apocryphon of John ( also part of the Nag Hammadi library ) has been useful in studying the prevailing attitudes in the second century, and questions of authorship regarding the Book of revelation, given that it refers to Revelation 1: 19, but is mostly about the post ascension teachings of Jesus in a vision, not a narrative of his life.

Similarly, the side bowling second tries to bowl out the second team for less than the target score in order to win.

Similarly, Tertullian argued that second marriage, by one who was made freed from the first by death, " will have to be termed no other than a species of fornication ," partly based on the reasoning that such involves desiring to marry a women out of sexual ardor.