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I want to use R in Python, as provided by the module Rpy2. I notice that R has very convenient operations by which you can extract the specific columns or lines. How could I achieve such a function by Python scripts?My idea is to create an R vector and add those wanted elements into this vector so that the final vector is the same as that in R. I created a seq, but it seems that it has an initial digit 1, so the final result would always start with the digit 1, which is not what I want.

So, is there a better way to do this?

Null Spaces of Matrices Description. Given a matrix, M, find a matrix N giving a basis for the (left) null space. That is crossprod(N, M) = t(N)%.% M is an all-zero matrix and N has the maximum number of linearly independent columns. Usage Null(M) Arguments. To create a vector from a simple sequence of integers, for example, you use the colon operator (:) in R. The code 3:7 gives you a vector with the numbers 3 to 7, and 4:-3 creates a vector with the numbers 4 to –3, both in steps of 1. To make bigger or smaller steps.

In mathematics, given a vector spaceX with an associated quadratic formq, written (X, q), a null vector or isotropic vector is a non-zero element x of X for which q(x) = 0.

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In the theory of realbilinear forms, definite quadratic forms and isotropic quadratic forms are distinct. They are distinguished in that only for the latter does there exist a nonzero null vector.

A quadratic space (X, q) which has a null vector is called a pseudo-Euclidean space.

A pseudo-Euclidean vector space may be decomposed (non-uniquely) into orthogonal subspacesA and B, X = A + B, where q is positive-definite on A and negative-definite on B. The null cone, or isotropic cone, of X consists of the union of balanced spheres:

${\displaystyle \bigcup _{r\ge 0}\{x=a+b:q(a)=-q(b)=r,a\in A,b\in B\}.}$

The null cone is also the union of the isotropic lines through the origin.

Examples[edit]

The light-like vectors of Minkowski space are null vectors.

The four linearly independentbiquaternionsl = 1 + hi, n = 1 + hj, m = 1 + hk, and m^∗ = 1 – hk are null vectors and { l, n, m, m^∗ } can serve as a basis for the subspace used to represent spacetime. Null vectors are also used in the Newman–Penrose formalism approach to spacetime manifolds.^[1]

A composition algebrasplits when it has a null vector; otherwise it is a division algebra.

In the Verma module of a Lie algebra there are null vectors.

References[edit]

1. ^Patrick Dolan (1968) A Singularity-free solution of the Maxwell-Einstein Equations, Communications in Mathematical Physics 9(2):161–8, especially 166, link from Project Euclid

• Dubrovin, B. A.; Fomenko, A. T.; Novikov, S. P. (1984). Modern Geometry: Methods and Applications. Translated by Burns, Robert G. Springer. p. 50. ISBN0-387-90872-2.
• Shaw, Ronald (1982). Linear Algebra and Group Representations. 1. Academic Press. p. 151. ISBN0-12-639201-3.
• Neville, E. H. (Eric Harold) (1922). Prolegomena to Analytical Geometry in Anisotropic Euclidean Space of Three Dimensions. Cambridge University Press. p. 204.