Scalar & Vector

In linear algebra, real numbers are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector. More generally, a vector space may be defined by using any field instead of real numbers, such as complex numbers. Then the scalars of that vector space will be the elements of the associated field.  A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms.

Introduction to Vectors

Vector Basic - Algebra Representation

Vector Basic - Algebra Representation part 2

Magnitude and Direction of a Vector, Example 1

Magnitude and Direction of a Vector, Example 2

Magnitude and Direction of a Vector, Example 3

Finding the Vector Equation of a Line

Vectors - Finding Magnitude or Length

Vector Basics : Drawing Vectors- Vector Addition

Vector Addition and Scalar Multiplication, Example 1

Vector Addition and Scalar Multiplication, Example 2

Vectors - the Dot Product

The Cross Product

Dot vs Cross Product

The Span of a Set of Vectors

Procedure to Find a Basis for a Set of Vectors

Gradient, Divergence and Curl (part 1/3)

Gradient, Divergence and Curl (part 2/3)

Gradient, Divergence and Curl (part 3/3)