MATHEMATICS  RESOURCE  CENTER
DEPARTMENT OF MATHEMATICS
INDIAN INSTITUTE OF TECHNOLOGY BOMBAY, INDIA

 

 

CHAPTER 1: FROM GEOMETRY TO ALGEBRA-1 THE EUCLIDEAN SPACE R


  Applet 1.1
Localized Vector
    Applet 1.2
Addition of Two Vectors
 
Applet 1.3
Associativity of Sum of Vectors
       Applet 1.4
 Scalar Multiplication of Vectors
 
       Applet 1.5
        Vector Equation of a Line
 
Applet 1.6
    Vector Equation of a Plane
  Applet 1.7 Midpoints of a Quadrilateral form Parallelogram  
Applet 1.8 Medians of Triangles are Concurrent and Divide Medians in 2:1  
   Applet 1.9
Quiz

CHAPTER 2: SYSTEM OF LINEAR EQUATION

 
     Applet 2.0
      Matrix Addition
 
Applet 2.0.1
 Matrix Multiplication - I
 
 
Applet 2.0.2
 Matrix Multiplication - II
  
  Applet 2.1 Algorithm
 for Row Echelon Form (Demo)
 
Applet 2.2
 Algorithm for Row Echelon Form
 
  Applet 2.3
 Inverse Matrix (Demo)
  Applet 2.4
Inverse of Matrix
 
Applet 2.5
Row Echelon Form
 
  Applet 2.6
LU Decomposition

CHAPTER 3: RANK OF A MATRIX

   
Applet 3.1
Linear Span of Vectors
 
Applet 3.2
 Linear Combination of Vectors
 
  Applet 3.3
 Rank of Matrix

CHAPTER 4: DETERMINANTS

 
  Applet 4.1
 Additive Property of Determinant
 
Applet 4.2  Multiplicative
Property of Determinant
 
Applet 4.3
 Determinant for 3*3 Matrix

CHAPTER 5: VECTOR SPACES , BASES AND DIMENSIONS

 
  Applet 5.1
 Linear Span of Vectors
 
Applet 5.2  Linear
Dependence or Independence on R
 
Applet 5.3 Co-ordinates
 with respect to Change of Basis

CHAPTER 6: LINEAR TRANSFORMATIONS

  
Applet 6.1
 Linear Transformations
 
Applet 6.2 Examples
 of Linear Transformations
 
Applet 6.3 Examples
  of Linear Transformations
  
Applet 6.3 Examples
 of Linear Transformations
 
Applet 6.5
 Change in Matrix Representation
 
 

CHAPTER 7: FROM GEOMETRY TO ALGEBRA- II INNER PRODUCT SPACES

  
Applet 7.1
 Inner  Product
 
Applet 7.2
 Commutative Law of Inner Product
 
Applet 7.3
 Distributive Law of Inner Product
  
  Applet 7.4 Algorithm
 Cauchy-Schwartz Inequality
 

 
 
 

CHAPTER 8: ORTHOGONAL PROJECTIONS AND ORTHONORMAL BASIS

 
Applet 8.1
 Constructing Orthonormal Basis
 
Applet 8.2
 Gram Schmidt Orthonormalisation
 
 
 
 

CHAPTER 9: ISOMETRICS AND EIGENVALUES

  
Applet 9.1
 Isometrics of R2
 
Applet 9.2
 Isometric of R3
 
Applet 9.3
 Eigen Values and Eigen Vectors

CHAPTER 10: DIAGONALIZATION AND SPECTRAL THEOREM

CHAPTER 11: APPLICATIONS OF DIAGONALIZATION

CHAPTER 12: APPLICATION OF LINEAR TRANSFORMATIONS IN COMPUTER GRAPHICS

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