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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

Outer Product

By Kardi Teknomo, PhD.

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Vector outer product is denoted by Outer Productor Outer Product. Vector outer product is also called vector matrix product because the result of the vector multiplication is a matrix. It can only be performed for two vectors of any size, not necessarily the same size.

Algebraically, the vector outer product is a multiplication of a column vector by a row vector Outer Productto obtain a matrix provided by the formula below
Outer Product
Suppose we have Outer ProductandOuter Product, the vector outer products are
Outer Product
Outer Product

Try to experiment with the interactive program below. Given two vectors, not necessarily at the same dimension, the program will produce the matrix outer product. If you click “Random Example” button, the program will generate random input vectors in the right format.

vector x vector y


Some important properties of vector outer product are

  • Vector outer product is a not commutative operation. If you reverse the order you will get different result and even different sizeOuter Product.
  • If matrix is the results of a vector productOuter Productthen multiplication of that matrix with the second factor produces a vector of the first factor scaled by the square norm of the second factorOuter Product.

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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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