Contents

1. General Vector Spaces     

1. Introduction  

2. Real Vector Spaces  

3. Euclidean n-space   

4. Subspaces of a Vector Space     

5. Linear Combination and Linear Span    

6. Linear Independence 

7. Basis and Dimension 

8. Row Space, Column Space, Null Space   

9. Rank and Nullity    

2. Eigen Values and Eigen Vectors

1. Introduction  

2. Eigen Values and Eigen Vectors  

3. Diagonalization     

4. Quadratic Forms     

3. Linear Transformations

1. Introduction  

2. Linear Transformation     

3. Kernel and Range of a Linear Transformation 

4. Inverse Linear Transformation   

5. Matrix of General Linear Transformation     

4. Groups and Coding   

1. Introduction  

2. Binary Operation and General Properties     

3. Groups  

4. Quotient Group

5. Properties of Distance Function 

6. Group Codes   

7. Additional Results from Boolean Matrices    

8. Decoding and Error Correction   

9. Public Key Cryptography