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
What is a matrix and why do we need matrix?
When you have a numerical data, you may want to put your data into a table.
When you give name to your data table which consists of horizontal rows and vertical columns and think of it as one entity, you have a compact form that make it easier to manipulate your data and to automate the operations on your data using fast and efficient procedures to find the solution of your problem.
A collection of numerical data which is organized into rows and columns is called a matrix. A matrix is rectangular array of elements. A matrix is defined by its size that is the number of rows and the number of columns. We always write matrix size as number of rows first and then the number of columns. A square matrix happens when the number of rows is equal to the number of columns, the size can be written as one number called order of the matrix, that is equal to the number of rows = the number of columns.
Based on the matrix size, we can give name:
In many modern books and journal papers, a matrix usually has notation of a bold uppercase roman letter, such as,,, …, while a vector is written as bold lowercase roman letter such as,,, …, . The entry element of a matrix or a vector is a scalar, usually denoted as lowercase roman letter.
The following are some examples of useful ways to organize things into matrix:
Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\