What is the matrix $P$ such that $P^{-1}AP = D$ is diagonal?
$begingroup$
How do I get the matrix $P$ if $P^{-1}AP=D$ is diagonal matrix and
$$A=
begin{bmatrix}
1 & 2 \
0 & 4
end{bmatrix}?
$$
linear-algebra
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
$endgroup$
|
show 1 more comment
$begingroup$
How do I get the matrix $P$ if $P^{-1}AP=D$ is diagonal matrix and
$$A=
begin{bmatrix}
1 & 2 \
0 & 4
end{bmatrix}?
$$
linear-algebra
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
$endgroup$
1
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
1
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
1
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11
|
show 1 more comment
$begingroup$
How do I get the matrix $P$ if $P^{-1}AP=D$ is diagonal matrix and
$$A=
begin{bmatrix}
1 & 2 \
0 & 4
end{bmatrix}?
$$
linear-algebra
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
$endgroup$
How do I get the matrix $P$ if $P^{-1}AP=D$ is diagonal matrix and
$$A=
begin{bmatrix}
1 & 2 \
0 & 4
end{bmatrix}?
$$
linear-algebra
linear-algebra
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
edited Nov 29 '18 at 7:45
Rócherz
2,7762721
2,7762721
asked Nov 29 '18 at 7:36
faisalfaisal
274
asked Nov 29 '18 at 7:36
faisalfaisal
274
asked Nov 29 '18 at 7:36
faisalfaisal
274
274
1
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
1
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
1
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11
|
show 1 more comment
1
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
1
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
1
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11
1
1
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
1
1
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
1
1
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
As suggested in hints $A $ is diagonisable. Matrix $D $ will have eigenvelues of $A $ along the diagonal, while $P $ contains the corresponding eigenvectors (as its columns). You can solve for eigenvalues and eigenvectors in the usual way. Given the simple form of $A $, it is immediately clear that it has two distinct eigenvalues, $1,4$ (so in particular it is diagonisable).
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
$endgroup$
add a comment |
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1 Answer
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1 Answer
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oldest
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$begingroup$
As suggested in hints $A $ is diagonisable. Matrix $D $ will have eigenvelues of $A $ along the diagonal, while $P $ contains the corresponding eigenvectors (as its columns). You can solve for eigenvalues and eigenvectors in the usual way. Given the simple form of $A $, it is immediately clear that it has two distinct eigenvalues, $1,4$ (so in particular it is diagonisable).
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
$endgroup$
add a comment |
$begingroup$
As suggested in hints $A $ is diagonisable. Matrix $D $ will have eigenvelues of $A $ along the diagonal, while $P $ contains the corresponding eigenvectors (as its columns). You can solve for eigenvalues and eigenvectors in the usual way. Given the simple form of $A $, it is immediately clear that it has two distinct eigenvalues, $1,4$ (so in particular it is diagonisable).
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
$endgroup$
add a comment |
$begingroup$
As suggested in hints $A $ is diagonisable. Matrix $D $ will have eigenvelues of $A $ along the diagonal, while $P $ contains the corresponding eigenvectors (as its columns). You can solve for eigenvalues and eigenvectors in the usual way. Given the simple form of $A $, it is immediately clear that it has two distinct eigenvalues, $1,4$ (so in particular it is diagonisable).
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
$endgroup$
As suggested in hints $A $ is diagonisable. Matrix $D $ will have eigenvelues of $A $ along the diagonal, while $P $ contains the corresponding eigenvectors (as its columns). You can solve for eigenvalues and eigenvectors in the usual way. Given the simple form of $A $, it is immediately clear that it has two distinct eigenvalues, $1,4$ (so in particular it is diagonisable).
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
answered Nov 29 '18 at 8:22
AnyADAnyAD
2,108812
2,108812
add a comment |
add a comment |
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1
$begingroup$
Do you know what the entries of $D$ are, and more specifically, what they are called? That's a hint.
$endgroup$
– Arthur
Nov 29 '18 at 7:44
$begingroup$
yes i do, all the entries are 0 except the diagonal is leading ones
$endgroup$
– faisal
Nov 29 '18 at 7:48
1
$begingroup$
Yes, but the diagonal entries: what are they?
$endgroup$
– Arthur
Nov 29 '18 at 8:02
$begingroup$
no it's not given they just said D is diagonal matrix
$endgroup$
– faisal
Nov 29 '18 at 8:05
1
$begingroup$
Find eigenvectors of this matrix. Eigenvalues you can list immediately.
$endgroup$
– Widawensen
Nov 29 '18 at 8:11