non-zero vector

A non-zero vector which is perpendicular to the plane.

There is no single continuous function that can do this for all non-zero vector inputs.

Then there exist non-zero vectors and such that and .

In other words, the algorithm should output a non-zero vector v such that .

Any non-zero vector of an irreducible representation is cyclic.

In both these examples, every non-zero vector has an inverse, making them both division algebras.

When we work in modulo-two arithmetic, many non-zero vectors are indeed orthogonal % perpendicular to themselves!

However, non-zero vectors in a cyclic representation may fail to be cyclic.

As the scalar 1 fixes no non-zero vector, these two groups are isomorphic to subgroups of Co.

Alternatively, each number, when written in binary, can be identified with a non-zero vector of length three over the binary field.

The parity-check matrix contains, as its columns, all the $N$ non-zero vectors of length $M$ bits.

A seminorm, on the other hand, is allowed to assign zero length to some non-zero vectors (in addition to the zero vector).

For non-zero vectors, we can then normalize the vectors by dividing out their sizes as shown above:

A natural description of an 1-subspace is the scalar multiplication of one non-zero vector v to all possible scalar values.

For example in the surface case, an everywhere non-zero vector field can exist on an orientable compact surface only for the torus.

Correspondingly, we will say that non-zero vectors 'x', 'y' of 'V' are orthogonal if and only if their inner product is zero.

A root system in V is a finite set Φ of non-zero vectors (called roots) that satisfy the following conditions:

A normed division algebra additionally must be finite-dimensional, and have the property that every non-zero vector has a unique multiplicative inverse.

A vector that is the sum of two or more non-zero vectors belonging to different eigenspaces will be tilted towards the eigenspace with largest eigenvalue.

A one dimensional vector subspace consists of a non-zero vector and all of its scalar multiples.

A common problem in computer graphics is to generate a non-zero vector in R that is orthogonal to a given non-zero one.

The versor (or normalized vector) of a non-zero vector is the unit vector codirectional with :

For a given pair (A, B) of matrices, and a given non-zero vector x, the generalized Rayleigh quotient is defined as:

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero.

Similarly, a normed space is Archimedean if a sum of terms, each equal to a non-zero vector , has norm greater than one for sufficiently large .