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
When we are dealing with ordinary number, when we say then we can obtainas long as. We write it asor. For example, the inverse of 2 is ½. Matrix inverse is similar to division operation in ordinary numbers. Suppose we have matrix multiplication such that the result of matrix product is an identity matrix . If such matrix exists, then that matrix is unique and we can write or we can also write.
Matrix inverse exists only for a square matrix (that is a matrix that has the same number of rows and columns). Unfortunately, matrix inverse does not always exist. Thus, we give name that a square matrix is singular if that matrix does not have an inverse matrix (remember a single person does not have a spouse). When a square matrix has an inverse, it is called non-singular matrix.
Because matrix inverse is a very important operation, in linear algebra, there are many ways to compute matrix inverse.
The interactive program below is using numerical methods. As this is an educational program, I limit the matrix size to square matrix of medium size up to order 10. Random Example button will create new random input matrix.
Some important properties of matrix inverse are
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\