Finding the Orthogonal Projection from a Matrix where $ a_ij = vec v_icdot vec v_j$ Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)A question about subspacesEntries of a positive definite symmetric matrix as inner productsGoing from an arbitrary basis $mathbbB_u$ to an ON-basis $mathbbB_v$ in $mathbbR^3$Find orthonormal basis of $mathbbR^3$ with a given span of two basis vectorsName of outer “product” of two vectors with exponentiation instead of multiplicationFind the maximum possible $k$ s.t. $langle v_i,v_jrangleleq 0$ for all $ineq j$.If I have a diagonalized matrix with degenerate eigenvalues, how do I generate an orthonormal set of vectors?why is $ vec u bullet vec v = u_1v_1 + u_2v_2$?Prove that every $3$ of $ 4$ vectors of $2$- planes are linearly independent.Form of a matrix in a basis where some of the basis vectors are eigenvectors
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Finding the Orthogonal Projection from a Matrix where $ a_ij = vec v_icdot vec v_j$
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)A question about subspacesEntries of a positive definite symmetric matrix as inner productsGoing from an arbitrary basis $mathbbB_u$ to an ON-basis $mathbbB_v$ in $mathbbR^3$Find orthonormal basis of $mathbbR^3$ with a given span of two basis vectorsName of outer “product” of two vectors with exponentiation instead of multiplicationFind the maximum possible $k$ s.t. $langle v_i,v_jrangleleq 0$ for all $ineq j$.If I have a diagonalized matrix with degenerate eigenvalues, how do I generate an orthonormal set of vectors?why is $ vec u bullet vec v = u_1v_1 + u_2v_2$?Prove that every $3$ of $ 4$ vectors of $2$- planes are linearly independent.Form of a matrix in a basis where some of the basis vectors are eigenvectors
$begingroup$
I am working on a problem that is asking to find $operatornameproj_Vv_3$ where the matrix $$A=beginbmatrix 3&5&11\ 5&9&20\ 11&20&49endbmatrix
$$
has entries $a_ij=vec v_icdot vec v_j$.
I though that the simplest way to answer this question was to use the formula
$$ (u_1,x)u_1+(u_2,x)u_2 = proj_vx .$$
Since the question also asks to express the solution as a linear combination of $ v_1$ and $ v_2 $, I assumed that I could just plug the numbers in. I knew I had to make the vectors unit vectors so my equation looked something like this:
$ 3(5)(v2)+ 1/11(v3) $ This answer is not the correct answer but I am wondering if I am reading the matrix in the wrong way or if I am confused about the usage of the formula. Does someone have a better idea?
linear-algebra matrices projection
edited Apr 1 at 2:03
Martin Argerami
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
$endgroup$
add a comment |
$begingroup$
I am working on a problem that is asking to find $operatornameproj_Vv_3$ where the matrix $$A=beginbmatrix 3&5&11\ 5&9&20\ 11&20&49endbmatrix
$$
has entries $a_ij=vec v_icdot vec v_j$.
I though that the simplest way to answer this question was to use the formula
$$ (u_1,x)u_1+(u_2,x)u_2 = proj_vx .$$
Since the question also asks to express the solution as a linear combination of $ v_1$ and $ v_2 $, I assumed that I could just plug the numbers in. I knew I had to make the vectors unit vectors so my equation looked something like this:
$ 3(5)(v2)+ 1/11(v3) $ This answer is not the correct answer but I am wondering if I am reading the matrix in the wrong way or if I am confused about the usage of the formula. Does someone have a better idea?
linear-algebra matrices projection
edited Apr 1 at 2:03
Martin Argerami
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
$endgroup$
$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16
add a comment |
$begingroup$
I am working on a problem that is asking to find $operatornameproj_Vv_3$ where the matrix $$A=beginbmatrix 3&5&11\ 5&9&20\ 11&20&49endbmatrix
$$
has entries $a_ij=vec v_icdot vec v_j$.
I though that the simplest way to answer this question was to use the formula
$$ (u_1,x)u_1+(u_2,x)u_2 = proj_vx .$$
Since the question also asks to express the solution as a linear combination of $ v_1$ and $ v_2 $, I assumed that I could just plug the numbers in. I knew I had to make the vectors unit vectors so my equation looked something like this:
$ 3(5)(v2)+ 1/11(v3) $ This answer is not the correct answer but I am wondering if I am reading the matrix in the wrong way or if I am confused about the usage of the formula. Does someone have a better idea?
linear-algebra matrices projection
edited Apr 1 at 2:03
Martin Argerami
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
$endgroup$
I am working on a problem that is asking to find $operatornameproj_Vv_3$ where the matrix $$A=beginbmatrix 3&5&11\ 5&9&20\ 11&20&49endbmatrix
$$
has entries $a_ij=vec v_icdot vec v_j$.
I though that the simplest way to answer this question was to use the formula
$$ (u_1,x)u_1+(u_2,x)u_2 = proj_vx .$$
Since the question also asks to express the solution as a linear combination of $ v_1$ and $ v_2 $, I assumed that I could just plug the numbers in. I knew I had to make the vectors unit vectors so my equation looked something like this:
$ 3(5)(v2)+ 1/11(v3) $ This answer is not the correct answer but I am wondering if I am reading the matrix in the wrong way or if I am confused about the usage of the formula. Does someone have a better idea?
linear-algebra matrices projection
linear-algebra matrices projection
edited Apr 1 at 2:03
Martin Argerami
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
edited Apr 1 at 2:03
Martin Argerami
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
edited Apr 1 at 2:03
Martin Argerami
130k1184185
edited Apr 1 at 2:03
Martin Argerami
130k1184185
edited Apr 1 at 2:03
Martin Argerami
130k1184185
130k1184185
asked Mar 31 at 19:56
user3471031user3471031
314
asked Mar 31 at 19:56
user3471031user3471031
314
asked Mar 31 at 19:56
user3471031user3471031
314
314
$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16
add a comment |
$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16
$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16
$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The formula as you wrote it makes no sense. The correct version, since $V=operatornamespanv_1,v_2$, is
$$
operatornameproj_V(v_3)=fracv_3cdot v_1v_1cdot v_1,v_1+fracv_3cdot v_2v_2cdot v_2,v_2.
$$
Reading the four numbers from the matrix we get
$$
operatornameproj_V(v_3)=fraca_13a_11,v_1+fraca_23a_22,v_2=frac113,v_1+frac59,v_2.
$$
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
$endgroup$
add a comment |
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1 Answer
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1 Answer
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oldest
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active
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active
oldest
votes
$begingroup$
The formula as you wrote it makes no sense. The correct version, since $V=operatornamespanv_1,v_2$, is
$$
operatornameproj_V(v_3)=fracv_3cdot v_1v_1cdot v_1,v_1+fracv_3cdot v_2v_2cdot v_2,v_2.
$$
Reading the four numbers from the matrix we get
$$
operatornameproj_V(v_3)=fraca_13a_11,v_1+fraca_23a_22,v_2=frac113,v_1+frac59,v_2.
$$
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
$endgroup$
add a comment |
$begingroup$
The formula as you wrote it makes no sense. The correct version, since $V=operatornamespanv_1,v_2$, is
$$
operatornameproj_V(v_3)=fracv_3cdot v_1v_1cdot v_1,v_1+fracv_3cdot v_2v_2cdot v_2,v_2.
$$
Reading the four numbers from the matrix we get
$$
operatornameproj_V(v_3)=fraca_13a_11,v_1+fraca_23a_22,v_2=frac113,v_1+frac59,v_2.
$$
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
$endgroup$
add a comment |
$begingroup$
The formula as you wrote it makes no sense. The correct version, since $V=operatornamespanv_1,v_2$, is
$$
operatornameproj_V(v_3)=fracv_3cdot v_1v_1cdot v_1,v_1+fracv_3cdot v_2v_2cdot v_2,v_2.
$$
Reading the four numbers from the matrix we get
$$
operatornameproj_V(v_3)=fraca_13a_11,v_1+fraca_23a_22,v_2=frac113,v_1+frac59,v_2.
$$
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
$endgroup$
The formula as you wrote it makes no sense. The correct version, since $V=operatornamespanv_1,v_2$, is
$$
operatornameproj_V(v_3)=fracv_3cdot v_1v_1cdot v_1,v_1+fracv_3cdot v_2v_2cdot v_2,v_2.
$$
Reading the four numbers from the matrix we get
$$
operatornameproj_V(v_3)=fraca_13a_11,v_1+fraca_23a_22,v_2=frac113,v_1+frac59,v_2.
$$
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
answered Apr 1 at 1:59
Martin ArgeramiMartin Argerami
130k1184185
130k1184185
add a comment |
add a comment |
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$begingroup$
What is $v$ here?
$endgroup$
– amd
Apr 1 at 1:16