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 Nullity & Null Space

By Kardi Teknomo, PhD.

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A homogeneous linear system Matrix Nullity & Null Spacecan be thought as a linear transformation of a vector Matrix Nullity & Null Spacein Matrix Nullity & Null Spacedimensional space into zero vector in Matrix Nullity & Null Spacedimensional space.

The solution Matrix Nullity & Null Space of a homogeneous system of equations Matrix Nullity & Null Spaceis called the null space of Matrix Nullity & Null Space and the dimension of the null space is called the nullity ofMatrix Nullity & Null Space.

The dimension of the range and the null space of a matrix are related through fundamental relationshipMatrix Nullity & Null Space. Where Matrix Nullity & Null Space is the number of original unknowns.

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See also: rank through RREF, matrix rank, matrix range, solving system linear equations

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Preferable reference for this tutorial is

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


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