Determinant computation is equivalent to matrix powering
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It has been claimed in this paper (page 2 last paragraph) that Matrix powering is equivalent to determinant computation.
https://www.cse.iitk.ac.in/users/manindra/algebra/depth-four.pdf
Does anybody why is this the case?
complexity-theory matrices
asked 7 hours ago
grontimgrontim
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It has been claimed in this paper (page 2 last paragraph) that Matrix powering is equivalent to determinant computation.
https://www.cse.iitk.ac.in/users/manindra/algebra/depth-four.pdf
Does anybody why is this the case?
complexity-theory matrices
asked 7 hours ago
grontimgrontim
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
It has been claimed in this paper (page 2 last paragraph) that Matrix powering is equivalent to determinant computation.
https://www.cse.iitk.ac.in/users/manindra/algebra/depth-four.pdf
Does anybody why is this the case?
complexity-theory matrices
asked 7 hours ago
grontimgrontim
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
It has been claimed in this paper (page 2 last paragraph) that Matrix powering is equivalent to determinant computation.
https://www.cse.iitk.ac.in/users/manindra/algebra/depth-four.pdf
Does anybody why is this the case?
complexity-theory matrices
complexity-theory matrices
asked 7 hours ago
grontimgrontim
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
grontimgrontim
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
grontimgrontim
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 7 hours ago
grontimgrontim
1061
asked 7 hours ago
grontimgrontim
1061
1061
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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grontim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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2 Answers
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It states that matrix powering is computationaly equivalent to computation.
From another angle, Coppersmith–Winograd algorithm for matrix multiplication has complexity $mathcal O(n^{2.373})$ and the same complexity is for determinant computation by fast multiplication.
The result comes from Triangularization and inversion via fast multiplication by James R. Bunch and John E. Hopcroft
answered 5 hours ago
EvilEvil
7,78342446
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add a comment |
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Look at the paper by Stephen Cook (numbered $[3]$ in the references of the paper you have mentioned). There, in proposition $5.2$ in page $13$, he shows the "computational equivalence" between matrix powering and determinant computation (and other problems).
answered 5 hours ago
Don FanucciDon Fanucci
427311
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Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
add a comment |
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2 Answers
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2 Answers
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oldest
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$begingroup$
It states that matrix powering is computationaly equivalent to computation.
From another angle, Coppersmith–Winograd algorithm for matrix multiplication has complexity $mathcal O(n^{2.373})$ and the same complexity is for determinant computation by fast multiplication.
The result comes from Triangularization and inversion via fast multiplication by James R. Bunch and John E. Hopcroft
answered 5 hours ago
EvilEvil
7,78342446
$endgroup$
add a comment |
$begingroup$
It states that matrix powering is computationaly equivalent to computation.
From another angle, Coppersmith–Winograd algorithm for matrix multiplication has complexity $mathcal O(n^{2.373})$ and the same complexity is for determinant computation by fast multiplication.
The result comes from Triangularization and inversion via fast multiplication by James R. Bunch and John E. Hopcroft
answered 5 hours ago
EvilEvil
7,78342446
$endgroup$
add a comment |
$begingroup$
It states that matrix powering is computationaly equivalent to computation.
From another angle, Coppersmith–Winograd algorithm for matrix multiplication has complexity $mathcal O(n^{2.373})$ and the same complexity is for determinant computation by fast multiplication.
The result comes from Triangularization and inversion via fast multiplication by James R. Bunch and John E. Hopcroft
answered 5 hours ago
EvilEvil
7,78342446
$endgroup$
It states that matrix powering is computationaly equivalent to computation.
From another angle, Coppersmith–Winograd algorithm for matrix multiplication has complexity $mathcal O(n^{2.373})$ and the same complexity is for determinant computation by fast multiplication.
The result comes from Triangularization and inversion via fast multiplication by James R. Bunch and John E. Hopcroft
answered 5 hours ago
EvilEvil
7,78342446
edited 5 hours ago
answered 5 hours ago
EvilEvil
7,78342446
answered 5 hours ago
EvilEvil
7,78342446
answered 5 hours ago
EvilEvil
7,78342446
7,78342446
add a comment |
add a comment |
$begingroup$
Look at the paper by Stephen Cook (numbered $[3]$ in the references of the paper you have mentioned). There, in proposition $5.2$ in page $13$, he shows the "computational equivalence" between matrix powering and determinant computation (and other problems).
answered 5 hours ago
Don FanucciDon Fanucci
427311
$endgroup$
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
add a comment |
$begingroup$
Look at the paper by Stephen Cook (numbered $[3]$ in the references of the paper you have mentioned). There, in proposition $5.2$ in page $13$, he shows the "computational equivalence" between matrix powering and determinant computation (and other problems).
answered 5 hours ago
Don FanucciDon Fanucci
427311
$endgroup$
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
add a comment |
$begingroup$
Look at the paper by Stephen Cook (numbered $[3]$ in the references of the paper you have mentioned). There, in proposition $5.2$ in page $13$, he shows the "computational equivalence" between matrix powering and determinant computation (and other problems).
answered 5 hours ago
Don FanucciDon Fanucci
427311
$endgroup$
Look at the paper by Stephen Cook (numbered $[3]$ in the references of the paper you have mentioned). There, in proposition $5.2$ in page $13$, he shows the "computational equivalence" between matrix powering and determinant computation (and other problems).
answered 5 hours ago
Don FanucciDon Fanucci
427311
answered 5 hours ago
Don FanucciDon Fanucci
427311
answered 5 hours ago
Don FanucciDon Fanucci
427311
answered 5 hours ago
Don FanucciDon Fanucci
427311
427311
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
add a comment |
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
$begingroup$
Perhaps you should add the paper’s title, and if possible, a link.
$endgroup$
– Yuval Filmus
2 hours ago
add a comment |
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