

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 
Matrix Size & Validation (How to use the interactive programs in this tutorial)In this page, I will explain how you will input and validate the size of a matrix or a vector in the interactive programs of this Linear Algebra tutorial. First, your input must be numbers (real or integer), or a sequence of numbers (not string of words or other characters) separated by commas, or space or semicolon.
Example:
As an alternative form, you may also use space to replace comma.
It is equivalent to When you input the sequence of numbers above, you will get A vector or a matrix will have several rows. When you want to write a sequence of numbers on different rows, use semi colon to separate each rows. The last row’s semicolon is optional. A matrix or a vector 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 vector is always a column vector (with only one column). Thus, instead of comma, you need to use semicolon to separate each entry.
It will produce When you want to write a row vector (consists only one row), you separate the numbers by commas.
A matrix may have several rows and several columns. You can write a matrix or a vector as sequence of numbers, separated by commas in a row and semicolon to mark the end of each row. Optionally, you can also write it in a nice format using carriage return. Example: It is equivalent to Both of them will produce
A matrix must have equal number of entries for all rows. If you mistype the entries, the program will accept it not as a matrix and the matrix or vector operations on your input will produce error or wrong answer. That is why you need to validate your input in the interactive program below. Example:
Some of the interactive programs in this linear algebra tutorial may have options to show the output as approximate fractional format. If you click the random example button, you may obtain a number in with several decimal digits. If you check , the result will be in fraction. To separate the whole number from the fraction, the program is using under bar.
It will produce
Now you are ready to play around with this exciting linear algebra tutorial, you may use the Next and Previous Navigation or go directly from the left navigation bar, or you can go back to the index of this tutorial. 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\ 



