Kardi Teknomo
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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

Matrix Addition

By Kardi Teknomo, PhD.

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When we have two matrices, Matrix Additionand Matrix Additionthen the sum of the two matrices Matrix Additionis a matrix whose entry is equal to the sum of the corresponding entriesMatrix Addition.
Matrix addition works only when the two matrices have the same size and the result is also the same size as the input matrices.

Matrix Addition, Matrix Addition,
Matrix Addition

The interactive program below shows you the result of matrix addition. Your input must be two matrices of the same size (one matrix for each text box). Random Example will generate random matrices of the same size.



Some important properties of matrix addition are

  • Matrix addition is a commutative operation, that you can reverse the order and still get the same result Matrix Addition
  • Matrix addition is an associative operation, that is exchanging the parentheses (to say which order to be computed first) does not change the resultMatrix Addition .
  • Null matrix (or zero matrix) is a unique additive identity matrix such thatMatrix Addition. The null matrix has the same size as matrixMatrix Addition.
  • Transpose of the matrix addition is equal to the addition of their transposes Matrix Addition

See also: matrix subtraction, null matrix, matrix transpose

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This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\


© 2007 Kardi Teknomo. All Rights Reserved.
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