6 First Homomorphism theorem for vector spaces # Theorem 4.1.1 # Explained in Tamil

7 Internal direct sum # External direct sum # Theorem 4.1.2 # Explained in Tamil

1 Vector Space definition # Linear Algebra # Explained in Tamil

5 V/W is a vector space # quotient space # Linear Algebra # Explained in Tamil

10 L(S) contained in L (T) # L(S union T)= L(S)+L(T) # L(L(S)=L(S) # Lemma 4.2.2 # in Tamil

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If T is a Homomorphism of U onto V with kernel W, then V is isomorphic to U/W || In Tamil

16 - (A+B)/B is isomorphic to A/(A intersection B) # second isomorphic theorem # linear algebra

Fundamental theorem of homomorphism of group in Tamil

RP&LA |Unit 4|Vector Spaces|MA3355| Check whether the set is a Vector Space |Solved problem in Tamil

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21 Hom ( V,W) is a vector space # linear algebra # explained in Tamil

4 Subspace # vector space homomorphism # kernel # ker T is a subspace # isomorphism iff ker ={0}

RP & L A | Unit 4 |Vector Spaces | Basis and Dimension of the Homogeneous System | Problem in Tamil

Dual Space W is isomorphic to Quotient space (Dual Space V/ A (W) ) -Theorem -Dual Space -

Basis, Dimension of Vector Spaces and Linear Transformation in Tamil

dim V/W = dim V - dim W # vector space # linear algebra # lemma 4.2.6