Vector Operations

Description

Sage is capable of executing most vector operations, including dot products, cross products, and Euclidean norms.
For example. we can compute the dot product of $\mathbf u = (1, 3/2, -1)$ and $\mathbf v = (1, 8, -2)$,

(1)
\begin{align} \mathbf u \cdot \mathbf v = 1 \cdot 1 + \frac{3}{2} \cdot 8 + (-1) \cdot (-2) = 15. \end{align}

Sage Cell

Code

u=vector(QQ,[1, 3/2, -1])
v=vector(ZZ,[1, 8, -2])
u.dot_product(v)

Options

Option

We can calculate the cross product $\mathbf u \times \mathbf v$ of $\mathbf u = (1, 3/2, -1)$ and $\mathbf v = (1, 8, -2)$.

Code

u=vector(QQ,[1, 3/2, -1])
v=vector(ZZ,[1, 8, -2])
u.cross_product(v)

Option

We can calculate the Euclidean norm of $\mathbf v$ of $\mathbf v = (1, 8, -2)$.

Code

v=vector(ZZ,[1, 8, -2])
v.norm()

Tags

Primary Tags: vectors

Secondary Tags: dot product, cross product, Euclidean norm.

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Author: T. W. Judson

Date: 28 Jul 2018 20:50

Submitted by: Tom Judson

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