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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

Vector Subtraction

By Kardi Teknomo, PhD.
LinearAlgebra

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Two vectors of the same dimension (i.e. the same number of elements) can be subtracted from one another to produce a resultant vector that is also at the same dimension as the input vectors. Negative vector is a vector with the same magnitude as the input vector but with the opposite direction. Thus vector subtraction is equal to addition of the first vector to the negative of the second vector.

Algebraically, vector subtraction is done by subtracting the corresponding element of the vectorsVector Subtraction.

Example
Vector Subtraction, Vector Subtraction, Vector Subtraction

Geometrically, a line segment bounded by two points Vector Subtractionand Vector Subtractionis equal to vector subtraction of the two points.
Vector Subtraction


Subtraction of two vectors is equal to addition of the first vector to the negative of the second vector. Since a vector can be displaced to a parallel line to the line of application (i.e. a line containing the vector), we can reverse the direction of the second vector and displace it to a parallel line such that we can join the final point of the first vector to the initial point of the second vector as shown in the figure below.

Vector SubtractionVector Subtraction

The interactive program below show you the algebraic part of the vector subtraction. Your input must be two vectors of the same dimension (one vector for each text box) and the program will produce the result of vector subtraction.

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Properties

Some important properties of vector subtraction are

  • Vector subtraction is a non-commutative operation. If you can reverse the order you will not get the same result Vector Subtraction
  • The only vector equal to its own negative is the zero vector and the sum of a vector with its negative is the zero vector,Vector Subtraction

See also: vector addition

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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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