Is there anything special with a 3x3 matrix where the 3rd row is 0 0 1?
$begingroup$
I'm coding using p5.js and I'm looking at this method https://p5js.org/reference/#/p5/applyMatrix
Using that method, I can multiply my current matrix with any matrix of the form:
$$
begin{pmatrix}
a & c & e \
b & d & f \
0 & 0 & 1 \
end{pmatrix}
$$
by calling applyMatrix(a, b, c, d, e, f)
There is no method for multiplying any arbitrary matrix like:
$$
begin{pmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
end{pmatrix}
$$
Is there anything special with a matrix of that form? Is it possible to convert any arbitrary matrix (like the bottom matrix) into a matrix of that form?
matrices
edited Jan 18 at 3:46
Alex Provost
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
$endgroup$
|
show 1 more comment
$begingroup$
I'm coding using p5.js and I'm looking at this method https://p5js.org/reference/#/p5/applyMatrix
Using that method, I can multiply my current matrix with any matrix of the form:
$$
begin{pmatrix}
a & c & e \
b & d & f \
0 & 0 & 1 \
end{pmatrix}
$$
by calling applyMatrix(a, b, c, d, e, f)
There is no method for multiplying any arbitrary matrix like:
$$
begin{pmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
end{pmatrix}
$$
Is there anything special with a matrix of that form? Is it possible to convert any arbitrary matrix (like the bottom matrix) into a matrix of that form?
matrices
edited Jan 18 at 3:46
Alex Provost
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
$endgroup$
$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
1
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45
|
show 1 more comment
$begingroup$
I'm coding using p5.js and I'm looking at this method https://p5js.org/reference/#/p5/applyMatrix
Using that method, I can multiply my current matrix with any matrix of the form:
$$
begin{pmatrix}
a & c & e \
b & d & f \
0 & 0 & 1 \
end{pmatrix}
$$
by calling applyMatrix(a, b, c, d, e, f)
There is no method for multiplying any arbitrary matrix like:
$$
begin{pmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
end{pmatrix}
$$
Is there anything special with a matrix of that form? Is it possible to convert any arbitrary matrix (like the bottom matrix) into a matrix of that form?
matrices
edited Jan 18 at 3:46
Alex Provost
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
$endgroup$
I'm coding using p5.js and I'm looking at this method https://p5js.org/reference/#/p5/applyMatrix
Using that method, I can multiply my current matrix with any matrix of the form:
$$
begin{pmatrix}
a & c & e \
b & d & f \
0 & 0 & 1 \
end{pmatrix}
$$
by calling applyMatrix(a, b, c, d, e, f)
There is no method for multiplying any arbitrary matrix like:
$$
begin{pmatrix}
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
end{pmatrix}
$$
Is there anything special with a matrix of that form? Is it possible to convert any arbitrary matrix (like the bottom matrix) into a matrix of that form?
matrices
matrices
edited Jan 18 at 3:46
Alex Provost
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
edited Jan 18 at 3:46
Alex Provost
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
edited Jan 18 at 3:46
Alex Provost
15.4k22350
edited Jan 18 at 3:46
Alex Provost
15.4k22350
edited Jan 18 at 3:46
Alex Provost
15.4k22350
15.4k22350
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
asked Jan 18 at 3:31
DarkPotatoKingDarkPotatoKing
184
184
$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
1
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45
|
show 1 more comment
$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
1
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45
$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
1
1
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45
|
show 1 more comment
1 Answer
1
active
oldest
votes
$begingroup$
It is a standard way to represent an affine transformation of the plane; this is how it is used on the page you linked. The submatrix $A = begin{pmatrix} a & c \ b & d end{pmatrix}$ in your question represents the linear part of the affine transformation, and the extra column $t = begin{pmatrix} e \ f end{pmatrix}$ to the right corresponds to the translation part of the transformation. In full, the corresponding transformation maps a vector $v$ to the vector $Av + t$.
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It is a standard way to represent an affine transformation of the plane; this is how it is used on the page you linked. The submatrix $A = begin{pmatrix} a & c \ b & d end{pmatrix}$ in your question represents the linear part of the affine transformation, and the extra column $t = begin{pmatrix} e \ f end{pmatrix}$ to the right corresponds to the translation part of the transformation. In full, the corresponding transformation maps a vector $v$ to the vector $Av + t$.
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
$endgroup$
add a comment |
$begingroup$
It is a standard way to represent an affine transformation of the plane; this is how it is used on the page you linked. The submatrix $A = begin{pmatrix} a & c \ b & d end{pmatrix}$ in your question represents the linear part of the affine transformation, and the extra column $t = begin{pmatrix} e \ f end{pmatrix}$ to the right corresponds to the translation part of the transformation. In full, the corresponding transformation maps a vector $v$ to the vector $Av + t$.
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
$endgroup$
add a comment |
$begingroup$
It is a standard way to represent an affine transformation of the plane; this is how it is used on the page you linked. The submatrix $A = begin{pmatrix} a & c \ b & d end{pmatrix}$ in your question represents the linear part of the affine transformation, and the extra column $t = begin{pmatrix} e \ f end{pmatrix}$ to the right corresponds to the translation part of the transformation. In full, the corresponding transformation maps a vector $v$ to the vector $Av + t$.
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
$endgroup$
It is a standard way to represent an affine transformation of the plane; this is how it is used on the page you linked. The submatrix $A = begin{pmatrix} a & c \ b & d end{pmatrix}$ in your question represents the linear part of the affine transformation, and the extra column $t = begin{pmatrix} e \ f end{pmatrix}$ to the right corresponds to the translation part of the transformation. In full, the corresponding transformation maps a vector $v$ to the vector $Av + t$.
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
edited Jan 18 at 3:45
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
answered Jan 18 at 3:37
Alex ProvostAlex Provost
15.4k22350
15.4k22350
add a comment |
add a comment |
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$begingroup$
Do you have a question about math?
$endgroup$
– John Douma
Jan 18 at 3:34
$begingroup$
My question is about matrices not the coding itself, I just put the link there for context.
$endgroup$
– DarkPotatoKing
Jan 18 at 3:39
$begingroup$
Your question appears to be about some programming language.
$endgroup$
– John Douma
Jan 18 at 3:39
$begingroup$
You could fit your $3 times 3$ matrix into the larger matrix $$ pmatrix{1&2&3&0\4&5&6&0\7&8&9&0\0&0&0&1} $$ which I would say is a "matrix of that form"
$endgroup$
– Omnomnomnom
Jan 18 at 3:42
1
$begingroup$
@DarkPotatoKing It is used to represent affine transformations. (This is also hinted at in the page you linked.)
$endgroup$
– Alex Provost
Jan 18 at 3:45