Video Lectures By Prof. S. Kumaresan
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Found total 122 results. Displaying results from 76 to 80.
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76
Linear Maps 4
Linear Maps and Basis, Vector space of linear maps
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77
Linear Maps 5
Linear Maps, Linear isomorphism,
 is the product of the dimensions of V and W. We define linear isomorphism and give some examples. We point out the bijections used to construct vector space (in Esoteric Examples) are linear isomorphisms. Finally, we prove that if V and W are finite dimensional vector spaces, then a linear map f from V to W is a linear isomorphism iff it is one-one and iff it is onto. Our proof does not use Rank-Nullity theorem, but in stead uses many basic results one has learned so far. So, this may be an instructive proof. Later we shall prove it using the rank-nullity theorem./sddefault.jpg)
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78
Linear Maps 6
Linear Maps, Linear isomorphism,
 Being linearly isomorphic is an equivalence relation and (ii) a linear map f from V to W is a linear isomorphism iff it takes a basis of V to a basis of W (without the assumption of finite dimensionality by avoiding the rank-nullity theorem). We also show that any finite dimensional vector spaces of the same dimension are linearly isomorphic./sddefault.jpg)
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79
Linear Maps 7
Ordered basis, system of coordinates, transition matrices
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80
Linear Maps 8
Matrix representation of a linear map
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