 |
|
|
|
|
|
||||||||||||
|
|||||||||||||||||
 |
 |
|
|
||||||||||||||
 |
 |
 |
|
|
|||||||||||||
 |
|
||||||||||||||||
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 (Gauss-Jordan) 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 |
Vector Scalar Multiple Multiplication of a vector
The interactive program below show you algebraic of vector scalar multiple. Your input must be a vector and the program will produce the result of vector scalar multiple. PropertiesSome important properties of vector scalar multiple are
See also: Eigen value & Eigen vector, matrix scalar multiple 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\ |
|||||||||||||
|
||||||||||||||
|
||||||||||||||
by a scalar 
will change the magnitude of the vector 
times. The direction of the scalar multiple 
is the same as the input vector
if 
and the opposite direction if
. The magnitude of the scalar multiple is stretched when 
and shrink when 
.The line of application of the vector does not change, they are collinear (there is no distinction between parallel and collinear in vectors of our definition).
, 
, then 
, 
.
. 
.
and multiplication
. 
