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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

Diagonal Matrix

By Kardi Teknomo, PhD.
LinearAlgebra

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A diagonal matrix is a square matrix (the same number of rows and columns) whose entries on the diagonal elements are non-zero while all other off-diagonal elements are zero. Diagonal elements are the entries whose index row is equal to column Diagonal matrix

Example:
If Diagonal matrix then Diagonal matrix

The interactive program below will retain only the diagonal element of the input matrix. The Random Example will generate random square matrix of random order. This program is designed to confirm your basic understanding about diagonal matrix.


Diagonal matrix has several nice properties that the operation on a diagonal matrix is simply equal to the operation on each diagonal element. The operation includes any functions and derivatives but the most well known properties are the following:

  • When two matricesDiagonal matrixandDiagonal matrixare both diagonal matrices, then their matrix multiplication is commutative (which is not true for matrices in general) Diagonal matrix
  • Exponential of a diagonal matrix is equal to exponential of each diagonal element
    Example
    Diagonal matrix
  • Power of a diagonal matrix is equal to power of each diagonal element
    Example
    Diagonal matrix
  • Inverse of a diagonal matrix is equal to reciprocal of each diagonal element
    Example
                    Diagonal matrix

See also: Trace, Is diagonal matrix, diagonalization

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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\

 

 
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