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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 Addition Two or more vectors of the same dimension (i.e. the same number of elements) can be added together to produce a resultant vector that is also at the same size as the input vectors. Algebraically, summation of two vectors is done by adding each element of the vectors Example Geometrically, summation of two vectors is performed by joining the final point of the first vector to the initial point of the second vector. As a vector can be displaced to a parallel line to the line of application (i.e. a line containing the vector), we can also create parallelogram to produce the resultant vector as shown in the figure below.
The interactive program below show you the algebraic part of the vector addition. Your input must be two vectors of the same dimension (one vector for each text box) and the program will produce the result of vector addition.
PropertiesSome important properties of vector addition are
See also: matrix subtraction, vector subtraction, null 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\ |
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. Geometrically, summation of vectors that produce zero-vector will for a closed polygon.