Similarly, if n is divisible by 3, and m was already a prime distinct from 3, then n − m would also be coprime to 3 and thus be slightly more likely to be prime than a general number.

Similarly, the limit superior of ( x < sub > n </ sub >) is defined by

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

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

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

Similarly, the E < sub > n </ sub > for even n look similar ( but not identical ) to each other after a simple division by n !.

Similarly, under the generalized Riemann hypothesis, the Miller – Rabin test can be turned into a deterministic version ( called Miller's test ) with runtime Õ (( log n )< sup > 4 </ sup >).

Similarly, mathematicians often describe Fermat's Last Theorem as asserting that there are no nontrivial integer solutions to the equation when n is greater than 2.

Similarly, the 29 minuscule forms ( lowercase or small letters ) are: a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, å, ä, and ö.

Similarly, allowing n > 0 here, we obtain

* Similarly, the free group F < sub > n </ sub > has p < sup > n </ sup > − 1 subgroups of index p.

Similarly, roots of a polynomial are said to be degenerate if they coincide, since generically the n roots of an nth degree polynomial are all distinct.

( Similarly, X < sub > k </ sub > and x < sub > n </ sub > are implicitly periodic in N, so their subscripts are evaluated modulo N .) The remaining terms give:

Similarly, for any semi-normed vector space we can define the distance between two vectors u and v as ‖ u − v ‖.

Similarly the set of all vectors in which is rational for all i is a countable dense subset of ; so for every the-dimensional Euclidean space is separable.

To see this, the three corresponding normal vectors of the corner's perpendicular sides can be considered to form a basis ( a rectangular coordinate system ) ( x, y, z ) in which to represent the direction of an arbitrary incoming ray, b, c. When the ray reflects from the first side, say x, the ray's x component, a, is reversed to-a while the y and z components are unchanged, resulting in a direction of b, c. Similarly, when reflected from side y and finally from side z, the b and c components are reversed.

* Similarly, in a three-dimensional space, the dot product of vectors b, c and e, f is ad + be + cf.

Similarly one can show that the difference between two pseudovectors is a pseudovector, that the sum or difference of two polar vectors is a polar vector, that multiplying a polar vector by any real number yields another polar vector, and that multiplying a pseudovector by any real number yields another pseudovector.

Similarly, the product of translation matrices is given by adding the vectors:

Similarly, a phylogeographic approach will likely play a key role in understanding the vectors and spread of avian influenza ( HPAI H5N1 ), demonstrating the relevance of phylogeography to the general public.

Similarly, Alice and Bob may evaluate any linear combination of a and b, or of any finite set of vectors, and will generally get different answers.

Similarly, three-dimensional velocity vectors can be built into a single-dimensional velocity vector:

Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates can be written as:

Similarly, the momentum is a vector quantity and is represented by a boldface symbol:

* Similarly the even-graded element γ = − σ < sub > 1 </ sub > σ < sub > 2 </ sub > corresponds to a vector rotation of 180 °:

Similarly, if the reference axes were stretched in one direction, the components of the vector, like the co-ordinates, would reduce in an exactly compensating way.

Similarly the torque is a vector.

Similarly, biproducts exist in the category of vector spaces over a field.

Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces.

Similarly, if the reference axes were stretched in one direction, the components of the vector, like the co-ordinates, would reduce in an exactly compensating way.

Similarly, in both English start reading and Japanese 読み始める yomihajimeru " start -- read " " start reading ," the vector verbs start and 始める hajimeru " start " change according to tense, negation, and the like, while the main verbs reading and 読み yomi " reading " usually remain the same.

Similarly, if the Ricci curvature is negative in the direction of a given vector ξ, such a conical region in the manifold will instead have larger volume than it would in Euclidean space.

Similarly, it is a derivation on where is the set of vector fields on M:

Similarly, the knot vector usually ends with a knot of that multiplicity.

Similarly, an Intercontinental ballistic missile also targets a vector.

A highest weight module is a module generated by a weight vector v, subject to for all weights μ, and for all i. Similarly, a quantum group can have a lowest weight representation and lowest weight module, i. e. a module generated by a weight vector v, subject to for all weights λ, and for all i.

Similarly price is the vector of individual prices of goods and services.

Similarly, a triality between three vector spaces over a field F is a nondegenerate trilinear map

Similarly, a vector space with a seminorm is called a seminormed vector space.