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Rajkishor Patra (M.Sc, Jadavpur University)
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Show that two given matrices A and B are congruent. what is index and signature of Matrix.
Eigen Value of real symmetric matrix are all real. Real skew symmetric matrix are purely imaginary or zero. Eigen Value of orthogonal matrix are of unit modules.
• Eigen Value of real symmetric matrix are a...
Find the dimension of the vector space R over Q , C over R, R over R and C over C.Link below 👇
• Dimension of vector space R over Q , C ove...
Which of the following is a subspace of R^3? 2a+3b+5c=0 / 2a+3b+5c=1/ 2a+3b+5c=-1/ none of the above, where (a,b,c)€R^3.Link below 👇
• Which of the following is a subspace of R^...
For the subspace U={(0,0)(c d)} and V={(a,b)(c -c)} the dimU and dimV are given by..Link below 👇
• For the subspace U={(0,0)(c d)} and V={(a,...
A linear mapping T:R^3-R^3 is defined by T(x,y,z)=(x+y+z,x+z ,x+y),(x,y,z)€R^3. If the matrix of T relative to the order basis { (1,0,0),(0,1,0),(0,0,1)} of R^3 be A and the matrix of T relative to the order basis { (0,1,1), (1,0,1),(1,1,0)} of R^3 be B, show that A and B are similar matrices.Link below
• A linear mapping T:R^3-R^3 is defined by T...
Let V be a vector space of dimension n over a field Fand let T€L(V,V). Let the matrix of T relative to the order basis (alpha) of V be A and the matrix of T relative to the order basis (beta) of V be B. Then there exist a non singular matrix P such that B=P-1AP. (Proof)Link below 👇
• Let V be a vector space of dimension n ove...
Proof of a important theorem on linear operator related to rank and Nullity.Prove that rank of (T_2T_1) less or equal to min{ rank of T_2,rank of T_2} and rank of (T_2T_1)= rank(T_1) if T_2 is invertible.Link below 👇
• Prove that rank of (T_2T_1) less or equal ...
Solution of a problem of linear algebra,from Higher Algebra -SKMapa(Exercise -16).Link below 👇
• Find a linear mapping T:R^3-R^3 such that ...
Show that reflection about the line y=x is linear mapping.Link below 👇
• Reflection about the line y=x is a linear ...
Gram Schmidt process of orthogonalisation together with an example with details explanation.
Link below 👇
• Gram Schmidt process of orthogonalisation,...
Diagonalizabl linear operator. Link below 👇
• DIAGONALIZABLE LINEAR OPERATOR or DIAGONAL...
Rank Nullity theorem.Link below 👇
• RANKK NULLITY THEOREM (SYLVASTER'S LAW) ...
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