Vectors

An n-tuple defined on real numbers can also be called a vector. In physics and mathematics, a vector is a mathematical object that has either size, magnitude or length, and a direction. In SymPy, a vector is represented as a 1 x n row matrix or an n x 1 column matrix. The following program demonstrates the concept of vector computations in SymPy. It computes the transpose and norm of a vector:

from sympy import *
u = Matrix([[1,2,3]]) # a row vector = 1x3 matrix
v = Matrix([[4],
[5],    # a col vector = 3x1 matrix
[6]])
v.T # use the transpose operation to
u[1] # 0-based indexing for entries
u.norm() # length of u
uhat = u/u.norm() # unit-length vec in same dir as u
uhat
uhat.norm()

The next program demonstrates the concepts of dot product, cross product, and projection operations on vectors:

from sympy import *
u = Matrix([ 1,2,3])
v = Matrix([-2,3,3])
u.dot(v)

acos(u.dot(v)/(u.norm()*v.norm())).evalf()
u.dot(v) == v.dot(u)
u = Matrix([2,3,4])
n = Matrix([2,2,3])
(u.dot(n) / n.norm...