Factorized trace of matrix productName for diagonals of a matrixtrace of product of positive definite matrixtrace of matrix productmatrix product with trace zerotrace of a product of similar matricesEigenvalues of Matrix Product.Trace of matrix that is a product of 2 others.Name of matrix which is invariant in traceTrace of a matrix productTrace of symmetric matrix product
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Factorized trace of matrix product
Name for diagonals of a matrixtrace of product of positive definite matrixtrace of matrix productmatrix product with trace zerotrace of a product of similar matricesEigenvalues of Matrix Product.Trace of matrix that is a product of 2 others.Name of matrix which is invariant in traceTrace of a matrix productTrace of symmetric matrix product
$begingroup$
Are there any particular types of matrices for which: $tr(AB)=tr(A)tr(B)$.
linear-algebra matrices
asked Mar 15 at 5:07
freudefreude
1516
$endgroup$
add a comment |
$begingroup$
Are there any particular types of matrices for which: $tr(AB)=tr(A)tr(B)$.
linear-algebra matrices
asked Mar 15 at 5:07
freudefreude
1516
$endgroup$
1
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
1
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11
add a comment |
$begingroup$
Are there any particular types of matrices for which: $tr(AB)=tr(A)tr(B)$.
linear-algebra matrices
asked Mar 15 at 5:07
freudefreude
1516
$endgroup$
Are there any particular types of matrices for which: $tr(AB)=tr(A)tr(B)$.
linear-algebra matrices
linear-algebra matrices
asked Mar 15 at 5:07
freudefreude
1516
asked Mar 15 at 5:07
freudefreude
1516
asked Mar 15 at 5:07
freudefreude
1516
asked Mar 15 at 5:07
freudefreude
1516
asked Mar 15 at 5:07
freudefreude
1516
1516
1
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
1
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11
add a comment |
1
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
1
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11
1
1
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
1
1
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$tr(AB)=tr(A)tr(B)$$
$$Sigma_j,i a_ji b_ij=Sigma_j,i a_jj b_ii$$
$$Sigma_j,i a_ji b_ij - a_jj b_ii=0$$
From here I am trying to find a class of matrices. To start with, let us assume that we are dealing with diagonal matrices only.
$$Sigma_j,i a_ji b_ij delta_ij - a_jj b_ii=0$$
For 2x2 matrices:
$$a_11 b_11 + a_22 b_22 - (a_11 + a_22)(b_11 + b_22)=0$$
$$-a_11 b_22 - a_22 b_11 =0$$
$$-a_11 b_22 = a_22 b_11$$
answered Mar 16 at 2:52
freudefreude
1516
$endgroup$
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
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oldest
votes
$begingroup$
$$tr(AB)=tr(A)tr(B)$$
$$Sigma_j,i a_ji b_ij=Sigma_j,i a_jj b_ii$$
$$Sigma_j,i a_ji b_ij - a_jj b_ii=0$$
From here I am trying to find a class of matrices. To start with, let us assume that we are dealing with diagonal matrices only.
$$Sigma_j,i a_ji b_ij delta_ij - a_jj b_ii=0$$
For 2x2 matrices:
$$a_11 b_11 + a_22 b_22 - (a_11 + a_22)(b_11 + b_22)=0$$
$$-a_11 b_22 - a_22 b_11 =0$$
$$-a_11 b_22 = a_22 b_11$$
answered Mar 16 at 2:52
freudefreude
1516
$endgroup$
add a comment |
$begingroup$
$$tr(AB)=tr(A)tr(B)$$
$$Sigma_j,i a_ji b_ij=Sigma_j,i a_jj b_ii$$
$$Sigma_j,i a_ji b_ij - a_jj b_ii=0$$
From here I am trying to find a class of matrices. To start with, let us assume that we are dealing with diagonal matrices only.
$$Sigma_j,i a_ji b_ij delta_ij - a_jj b_ii=0$$
For 2x2 matrices:
$$a_11 b_11 + a_22 b_22 - (a_11 + a_22)(b_11 + b_22)=0$$
$$-a_11 b_22 - a_22 b_11 =0$$
$$-a_11 b_22 = a_22 b_11$$
answered Mar 16 at 2:52
freudefreude
1516
$endgroup$
add a comment |
$begingroup$
$$tr(AB)=tr(A)tr(B)$$
$$Sigma_j,i a_ji b_ij=Sigma_j,i a_jj b_ii$$
$$Sigma_j,i a_ji b_ij - a_jj b_ii=0$$
From here I am trying to find a class of matrices. To start with, let us assume that we are dealing with diagonal matrices only.
$$Sigma_j,i a_ji b_ij delta_ij - a_jj b_ii=0$$
For 2x2 matrices:
$$a_11 b_11 + a_22 b_22 - (a_11 + a_22)(b_11 + b_22)=0$$
$$-a_11 b_22 - a_22 b_11 =0$$
$$-a_11 b_22 = a_22 b_11$$
answered Mar 16 at 2:52
freudefreude
1516
$endgroup$
$$tr(AB)=tr(A)tr(B)$$
$$Sigma_j,i a_ji b_ij=Sigma_j,i a_jj b_ii$$
$$Sigma_j,i a_ji b_ij - a_jj b_ii=0$$
From here I am trying to find a class of matrices. To start with, let us assume that we are dealing with diagonal matrices only.
$$Sigma_j,i a_ji b_ij delta_ij - a_jj b_ii=0$$
For 2x2 matrices:
$$a_11 b_11 + a_22 b_22 - (a_11 + a_22)(b_11 + b_22)=0$$
$$-a_11 b_22 - a_22 b_11 =0$$
$$-a_11 b_22 = a_22 b_11$$
answered Mar 16 at 2:52
freudefreude
1516
answered Mar 16 at 2:52
freudefreude
1516
answered Mar 16 at 2:52
freudefreude
1516
answered Mar 16 at 2:52
freudefreude
1516
1516
add a comment |
add a comment |
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1
$begingroup$
$1times 1$ matrices?
$endgroup$
– Lord Shark the Unknown
Mar 15 at 6:15
$begingroup$
Thanks, are there any other classes?
$endgroup$
– freude
Mar 16 at 3:00
1
$begingroup$
Yes, such as the set of all upper triangular matrices with zero diagonals.
$endgroup$
– user1551
Mar 16 at 3:11