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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 Addition

By Kardi Teknomo, PhD.
LinearAlgebra

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Two or more vectors of the same dimension (i.e. the same number of elements) can be added together to produce a resultant vector that is also at the same size as the input vectors.

Algebraically, summation of two vectors is done by adding each element of the vectorsVector Addition.

Example
Vector Addition, Vector Addition, Vector Addition

Geometrically, summation of two vectors is performed by joining the final point of the first vector to the initial point of the second vector. As a vector can be displaced to a parallel line to the line of application (i.e. a line containing the vector), we can also create parallelogram to produce the resultant vector as shown in the figure below.


Vector AdditionVector Addition

The interactive program below show you the algebraic part of the vector addition. 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 addition.

+

Properties

Some important properties of vector addition are

  • Vector addition is a commutative operation. You can reverse the order of addition and still get the same result Vector Addition
  • Vector addition is an associative operation. Exchanging the parentheses (to say which order to be computed first) does not change the resultVector Addition .
  • Zero vector is a unique additive identity vector such thatVector Addition. Geometrically, summation of vectors that produce zero-vector will for a closed polygon.
    Vector Addition

See also: matrix subtraction, vector subtraction, null matrix

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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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