K.S. Narain , ICTP

lecture 3

Map between two vectors , Cauchy-Schwarz inequality and Orthogonalization Theorem

• The existence of unique map between two vectors and definition of linear map is given. (giving all properties)
• Cauchy-Schwarz inequality and complex vector and their properties with some examples are introduced.
• The notion of distance between two vectors mentioned.
• Orthogonalization Theorem and Graham Schmidt method by giving several examples were said.
• Transpose vector and its properties realized.
• Unitary group, unitary transformation ,parity transformation
• Definition of linear generator is explained.