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Title: Linear Algebra
Department: Mathematics
Author: Dr. K.C. Sivakumar
University: IIT Madras
Type: WebLink
Abstract: Systems of linear equations, Matrices, Elementary row operations, Row'reduced echelon matrices. Vector spaces, Subspaces, Bases and dimension, Ordered bases and coordinates.
Linear transformations, Rank'nullity theorem, Algebra of linear transformations, Isomorphism, Matrix representation, Linear functionals, Annihilator, Double dual, Transpose of a linear transformation.
Characteristic values and characteristic vectors of linear transformations, Diagonalizability, Minimal polynomial of a linear transformation, Cayley'Hamilton theorem, Invariant subspaces, Direct'sum decompositions, Invariant direct sums, The primary decomposition theorem, Cyclic subspaces and annihilators, Cyclic decomposition, Rational, Jordan forms.
Inner product spaces, Orthonormal bases, Gram'Schmidt process.
 
   
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