Two vectors of the same size can be added together by adding their corresponding elements, to form another vector of the same size, called the sum of the vectors. $\begin{bmatrix} 0 \\ 7 \\ 3 \end{bmatrix} + \begin{bmatrix} 1 \\ 2 \\ 0 \end{bmatrix} = \begin{bmatrix} 1 \\ 9 \\ 3 \end{bmatrix}$ Likewise, for substraction, the difference of two vectors is $\begin{bmatrix} 1 \\ 9 \end{bmatrix} - \begin{bmatrix} 1 \\ 1 \end{bmatrix} = \begin{bmatrix} 0 \\ 8 \end{bmatrix}$ …

Posted on

# Vectors Examples

An $$n$$-vector can be used to represent $$n$$ quantities or values in an application. A 2-vector can be used to represent a position in a 2-dimensional (2-D) space. A 3-vector can be used to represent a location in a 3-dimensional (3-D) space. Each entry of the vector gives a coordinate. When a vector is used to represent a displacement in space, it is typically drawn as an arrow. from mpl_toolkits import mplot3d import matplotlib. …

Posted on

# Vectors

A vector is an ordered finite list of numbers. They’re normally written as vertical arrays, surrounded by squared or curved brackets. $\begin{pmatrix} -1.1 \\ 0.0 \\ 3.6 \\ -7.2 \end{pmatrix}$ or $\begin{bmatrix} -1.1 \\ 0.0 \\ 3.6 \\ -7.2 \end{bmatrix}$ The elements (or entries, coefficients, components) of a vector are the values in the array. The size (or dimensions, or length) of the vector is the number of elements it contains; an $$n$$-dimensional vector (or n-vector) is a vector with $$n$$ elements in it. …

Posted on

# Double Integrals

The integration of a function of two variables is called iterated integration. The following is an example of a double integral: $\int_3^6 \int_{-1}^2 10xy^2 dxdy$ Because integrals can be thought of as “undoing” differentiation, the double integral can be interpreted as undoing a second partial derivative of a function. from sympy.abc import x, y from sympy import * expr = 10 * x * y**2 integrate(expr, (x, -1, 2), (y, 3, 6)) ## 945

Posted on

# Products

New products coming soon,

Posted on