Bilinear Maps and their relationships with dual bases Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Non degenerate bilinear formTensor product in multilinear algebraWhat does $[L]=[I]^-1[II]$ mean?Connection between dual maps and bilinear forms?Function of a dual space?How to prove that every dual linear operator of an operator on $L_2(mathbbR)$ shares its eigenvalues with its dual operatorInterpretation of transpose of a linear application from a matricial product point of viewProve: If $y_0,…,y_n$ are pairwise different real numbers, then the vectors $f_y_0,…,f_y_n$ form a basis of the dual space $V^*$Properties of External orthogonal sum of bilinear spacesChecking my Understanding of and Motivation behind Tensors
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Bilinear Maps and their relationships with dual bases
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Non degenerate bilinear formTensor product in multilinear algebraWhat does $[L]=[I]^-1[II]$ mean?Connection between dual maps and bilinear forms?Function of a dual space?How to prove that every dual linear operator of an operator on $L_2(mathbbR)$ shares its eigenvalues with its dual operatorInterpretation of transpose of a linear application from a matricial product point of viewProve: If $y_0,…,y_n$ are pairwise different real numbers, then the vectors $f_y_0,…,f_y_n$ form a basis of the dual space $V^*$Properties of External orthogonal sum of bilinear spacesChecking my Understanding of and Motivation behind Tensors
$begingroup$
I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.
Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,
f is dual bilinear maps iff M(f,T,S) is regular matrix.
(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)
bilinear-form dual-spaces dual-maps
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
$endgroup$
add a comment |
$begingroup$
I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.
Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,
f is dual bilinear maps iff M(f,T,S) is regular matrix.
(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)
bilinear-form dual-spaces dual-maps
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
$endgroup$
add a comment |
$begingroup$
I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.
Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,
f is dual bilinear maps iff M(f,T,S) is regular matrix.
(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)
bilinear-form dual-spaces dual-maps
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
$endgroup$
I have a theorem without proof. I have searched many books and tried on myself, but i still dont have the solution.
Let M and N F-vector spaces, T be a base of M ,S be a base of N such that dimension of M is equal with dimension of N and f:MxN->F be a bilinear transformation. Then,
f is dual bilinear maps iff M(f,T,S) is regular matrix.
(where M(f,T,S) is a matrix of f dual bilinear transformation according to the bases T and S.)
bilinear-form dual-spaces dual-maps
bilinear-form dual-spaces dual-maps
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
asked Mar 25 at 19:58
Ümit ErtuğrulÜmit Ertuğrul
11
11
add a comment |
add a comment |
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