Mixing
Is this matrix positive semidefinite (Symmetric matrix, with particular pattern)
$begingroup$
Let's consider a symmetric matrix A.
If for each row, the diagonal entry is equal or larger than the magnitude of any other element, that is
$$a_{ii} geq |a_{ij}| quadtext{for all rows } i text{ and entries } j , ,$$
then the matrix is positive semi-definite
matrices positive-semidefinite
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
add a comment |
$begingroup$
Let's consider a symmetric matrix A.
If for each row, the diagonal entry is equal or larger than the magnitude of any other element, that is
$$a_{ii} geq |a_{ij}| quadtext{for all rows } i text{ and entries } j , ,$$
then the matrix is positive semi-definite
matrices positive-semidefinite
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
add a comment |
$begingroup$
Let's consider a symmetric matrix A.
If for each row, the diagonal entry is equal or larger than the magnitude of any other element, that is
$$a_{ii} geq |a_{ij}| quadtext{for all rows } i text{ and entries } j , ,$$
then the matrix is positive semi-definite
matrices positive-semidefinite
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
Let's consider a symmetric matrix A.
If for each row, the diagonal entry is equal or larger than the magnitude of any other element, that is
$$a_{ii} geq |a_{ij}| quadtext{for all rows } i text{ and entries } j , ,$$
then the matrix is positive semi-definite
matrices positive-semidefinite
matrices positive-semidefinite
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
asked Jan 14 at 10:09
Tommaso BendinelliTommaso Bendinelli
14110
14110
add a comment |
add a comment |
1 Answer
1
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oldest
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$begingroup$
It's false, I've just this counterexample.
$$begin{pmatrix}
1 & 0.9 & 0.9 \
0.9 & 1 & 0.1 \
0.9 & 0.1 & 1
end{pmatrix}$$
is indefinite, since the eigenvalues are $0.9$ and $(21 pm sqrt{649})/20$.
From this answer:
Is this a positive semi- definite matrix
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It's false, I've just this counterexample.
$$begin{pmatrix}
1 & 0.9 & 0.9 \
0.9 & 1 & 0.1 \
0.9 & 0.1 & 1
end{pmatrix}$$
is indefinite, since the eigenvalues are $0.9$ and $(21 pm sqrt{649})/20$.
From this answer:
Is this a positive semi- definite matrix
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
add a comment |
$begingroup$
It's false, I've just this counterexample.
$$begin{pmatrix}
1 & 0.9 & 0.9 \
0.9 & 1 & 0.1 \
0.9 & 0.1 & 1
end{pmatrix}$$
is indefinite, since the eigenvalues are $0.9$ and $(21 pm sqrt{649})/20$.
From this answer:
Is this a positive semi- definite matrix
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
add a comment |
$begingroup$
It's false, I've just this counterexample.
$$begin{pmatrix}
1 & 0.9 & 0.9 \
0.9 & 1 & 0.1 \
0.9 & 0.1 & 1
end{pmatrix}$$
is indefinite, since the eigenvalues are $0.9$ and $(21 pm sqrt{649})/20$.
From this answer:
Is this a positive semi- definite matrix
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
$endgroup$
It's false, I've just this counterexample.
$$begin{pmatrix}
1 & 0.9 & 0.9 \
0.9 & 1 & 0.1 \
0.9 & 0.1 & 1
end{pmatrix}$$
is indefinite, since the eigenvalues are $0.9$ and $(21 pm sqrt{649})/20$.
From this answer:
Is this a positive semi- definite matrix
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
answered Jan 14 at 10:16
Tommaso BendinelliTommaso Bendinelli
14110
14110
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
add a comment |
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
$begingroup$
Rounding off to integers looks more beautiful (with only zeros and ones).
$endgroup$
– A.Γ.
Jan 14 at 10:19
add a comment |
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