Representing a function in vector form.
$begingroup$
As far as I understand, according to linear algebra, linear functions, both single and multivariable, can be represented in vector form.
For instance,
$$z = aw + bx + cy + d$$
can be rewritten as
$$z = begin{bmatrix}a & b&c &|& dend{bmatrix} cdot begin{bmatrix}w \ x \ y \ 1end{bmatrix}$$
My questions are:
- Am I correct with the above?
- Is it possible to rewrite the function $bbox[lightgray] {z = w^2 + x^2 + y^2 + 8}$ in vector form?
functions vectors multivariate-polynomial
asked Dec 29 '18 at 17:40
user366312user366312
648520
$endgroup$
add a comment |
$begingroup$
As far as I understand, according to linear algebra, linear functions, both single and multivariable, can be represented in vector form.
For instance,
$$z = aw + bx + cy + d$$
can be rewritten as
$$z = begin{bmatrix}a & b&c &|& dend{bmatrix} cdot begin{bmatrix}w \ x \ y \ 1end{bmatrix}$$
My questions are:
- Am I correct with the above?
- Is it possible to rewrite the function $bbox[lightgray] {z = w^2 + x^2 + y^2 + 8}$ in vector form?
functions vectors multivariate-polynomial
asked Dec 29 '18 at 17:40
user366312user366312
648520
$endgroup$
add a comment |
$begingroup$
As far as I understand, according to linear algebra, linear functions, both single and multivariable, can be represented in vector form.
For instance,
$$z = aw + bx + cy + d$$
can be rewritten as
$$z = begin{bmatrix}a & b&c &|& dend{bmatrix} cdot begin{bmatrix}w \ x \ y \ 1end{bmatrix}$$
My questions are:
- Am I correct with the above?
- Is it possible to rewrite the function $bbox[lightgray] {z = w^2 + x^2 + y^2 + 8}$ in vector form?
functions vectors multivariate-polynomial
asked Dec 29 '18 at 17:40
user366312user366312
648520
$endgroup$
As far as I understand, according to linear algebra, linear functions, both single and multivariable, can be represented in vector form.
For instance,
$$z = aw + bx + cy + d$$
can be rewritten as
$$z = begin{bmatrix}a & b&c &|& dend{bmatrix} cdot begin{bmatrix}w \ x \ y \ 1end{bmatrix}$$
My questions are:
- Am I correct with the above?
- Is it possible to rewrite the function $bbox[lightgray] {z = w^2 + x^2 + y^2 + 8}$ in vector form?
functions vectors multivariate-polynomial
functions vectors multivariate-polynomial
asked Dec 29 '18 at 17:40
user366312user366312
648520
asked Dec 29 '18 at 17:40
user366312user366312
648520
asked Dec 29 '18 at 17:40
user366312user366312
648520
asked Dec 29 '18 at 17:40
user366312user366312
648520
asked Dec 29 '18 at 17:40
user366312user366312
648520
648520
add a comment |
add a comment |
2 Answers
2
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$begingroup$
In the same vein as your example, one can write $$w^2+x^2+y^2+8=begin{bmatrix}w&x&y&1end{bmatrix}begin{bmatrix}1&0&0&0\0&1&0&0\0&0&1&0\0&0&0&8end{bmatrix}begin{bmatrix}w\x\y\1end{bmatrix}.$$
answered Dec 30 '18 at 0:38
amdamd
32k21053
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add a comment |
$begingroup$
If you let $$ u=<x,y,w>$$
Then $$z=u.u+8=||u||^2 +8$$
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
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2 Answers
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2 Answers
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$begingroup$
In the same vein as your example, one can write $$w^2+x^2+y^2+8=begin{bmatrix}w&x&y&1end{bmatrix}begin{bmatrix}1&0&0&0\0&1&0&0\0&0&1&0\0&0&0&8end{bmatrix}begin{bmatrix}w\x\y\1end{bmatrix}.$$
answered Dec 30 '18 at 0:38
amdamd
32k21053
$endgroup$
add a comment |
$begingroup$
In the same vein as your example, one can write $$w^2+x^2+y^2+8=begin{bmatrix}w&x&y&1end{bmatrix}begin{bmatrix}1&0&0&0\0&1&0&0\0&0&1&0\0&0&0&8end{bmatrix}begin{bmatrix}w\x\y\1end{bmatrix}.$$
answered Dec 30 '18 at 0:38
amdamd
32k21053
$endgroup$
add a comment |
$begingroup$
In the same vein as your example, one can write $$w^2+x^2+y^2+8=begin{bmatrix}w&x&y&1end{bmatrix}begin{bmatrix}1&0&0&0\0&1&0&0\0&0&1&0\0&0&0&8end{bmatrix}begin{bmatrix}w\x\y\1end{bmatrix}.$$
answered Dec 30 '18 at 0:38
amdamd
32k21053
$endgroup$
In the same vein as your example, one can write $$w^2+x^2+y^2+8=begin{bmatrix}w&x&y&1end{bmatrix}begin{bmatrix}1&0&0&0\0&1&0&0\0&0&1&0\0&0&0&8end{bmatrix}begin{bmatrix}w\x\y\1end{bmatrix}.$$
answered Dec 30 '18 at 0:38
amdamd
32k21053
answered Dec 30 '18 at 0:38
amdamd
32k21053
answered Dec 30 '18 at 0:38
amdamd
32k21053
answered Dec 30 '18 at 0:38
amdamd
32k21053
32k21053
add a comment |
add a comment |
$begingroup$
If you let $$ u=<x,y,w>$$
Then $$z=u.u+8=||u||^2 +8$$
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
If you let $$ u=<x,y,w>$$
Then $$z=u.u+8=||u||^2 +8$$
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
add a comment |
$begingroup$
If you let $$ u=<x,y,w>$$
Then $$z=u.u+8=||u||^2 +8$$
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
$endgroup$
If you let $$ u=<x,y,w>$$
Then $$z=u.u+8=||u||^2 +8$$
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
answered Dec 29 '18 at 17:49
Mohammad Riazi-KermaniMohammad Riazi-Kermani
42.2k42061
42.2k42061
add a comment |
add a comment |
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