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 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 vectors.
Geometrically, a line segment bounded by two points and is equal to vector subtraction of the two points.
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.
Some important properties of vector subtraction are
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\