Matrix Size & Validation
What is Vector?
Vector Scalar Multiple
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
What is a matrix?
Matrix Diagonal Is Diagonal Matrix?
Matrix Basic Operation
Is Equal Matrix?
Matrix Scalar Multiple
Elementary Row Operations
Finding inverse using RREF (Gauss-Jordan)
Finding Matrix Rank using RREF
Is Singular Matrix?
Matrix Generalized Inverse
Solving System of Linear Equations
Linear combination, Span & Basis Vector
Linearly Dependent & Linearly Independent
Change of basis
Matrix Nullity & Null Space
Matrix Eigen Value & Eigen Vector
Matrix Eigen Value & Eigen Vector for Symmetric Matrix
Similarity Transformation and Matrix Diagonalization
Singular Value Decomposition
Resources on Linear Algebra
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 vectors.
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.
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.
Some important properties of vector addition are
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\