

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 (GaussJordan) 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 
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. Since the meaning of each row and each column is well defined in each application, we can remove the definition and dealing only with the array of elements. The table above can be written as 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. Example: Example: 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:
Rate this tutorial or give your comments about this tutorial Preferable reference for this tutorial is Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\ 



