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Matrix Size & Validation
Vector Algebra
What is Vector?
Vector Norm
Unit Vector
Vector Addition
Vector Subtraction
Vector Scalar Multiple
Vector Multiplication
Vector Inner Product
Vector Outer Product
Vector Cross Product
Vector Triple Cross Product
Vector Triple Dot Product
Scalar Triple Product
Orthogonal & Orthonormal Vector
Cos Angle of Vectors
Scalar and Vector Projection
Matrix Algebra
What is a matrix?
Special Matrices
Matrix One
Null Matrix
Matrix Diagonal Is Diagonal Matrix?
Identity Matrix
Matrix Determinant
Matrix Sum
Matrix Trace
Matrix Basic Operation
Is Equal Matrix?
Matrix Transpose
Matrix Addition
Matrix Subtraction
Matrix Multiplication
Matrix Scalar Multiple
Hadamard Product
Horizontal Concatenation
Vertical Concatenation
Elementary Row Operations
Matrix RREF
Finding inverse using RREF (Gauss-Jordan)
Finding Matrix Rank using RREF
Matrix Inverse
Is Singular Matrix?
Linear Transformation
Matrix Generalized Inverse
Solving System of Linear Equations
Linear combination, Span & Basis Vector
Linearly Dependent & Linearly Independent
Change of basis
Matrix Rank
Matrix Range
Matrix Nullity & Null Space
Eigen System
Matrix Eigen Value & Eigen Vector
Symmetric Matrix
Matrix Eigen Value & Eigen Vector for Symmetric Matrix
Similarity Transformation and Matrix Diagonalization
Matrix Power
Orthogonal Matrix
Spectral Decomposition
Singular Value Decomposition
Resources on Linear Algebra

Unit Vector

By Kardi Teknomo, PhD.
LinearAlgebra

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A unit vector is a vector of unit length. Any non-zero vector can be normalized into a unit vector by a division of a vector by its norm, that isUnit Vector.
Note that unit vector is not equal to one vectorUnit Vector, it is the magnitude of the vector is one, not the elements.

 

Example:
Suppose we have vector Unit Vector
The norm of the vector isUnit Vector
Converting it to unit vector becomes Unit Vector
Now the norm of the unit vector is Unit Vector

The interactive program below will help you to convert your vector input into a unit vector of any positive dimension. The program will also show you the norm of input vector, norm of unit vector (which is always 1) and sum of the unit vector.

Report in rational format

Properties

Some important properties of unit vector are

  • The inner product of a unit vector to itself is oneUnit Vector.
  • Two unit vectors Unit Vectorand Unit Vectorare perpendicular to each other (orthogonal) if and only ifUnit Vector.
  • In an Euclidean space, the standard unit vectors that orthogonal to each other has name:
    o   unit vector of the first dimension is Unit Vector
    o   unit vector of the second dimension is Unit Vector
    o   unit vector of the third dimension is Unit Vector
    Unit Vector
  • The dot products of the standard unit vector:
    o   Dot product of the same standard unit vector is oneUnit Vector
    o   Dot product of the perpendicular standard unit vector is zeroUnit Vector
  • The cross product of the standard unit vectors:
    o   Cross product of the same standard unit vector is zeroUnit Vector
    o   Cross product of the perpendicular standard unit vector form a cycle Unit Vector;Unit Vector;Unit Vector;Unit Vector;Unit Vector;Unit Vector·          

See also: dot product, cross product, vector norm, basis vector

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This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\

 

 
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