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0

$begingroup$

As far as I understand, the matrix

$$
beginbmatrix
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
endbmatrix
$$

refers to a linear transformation of the unit vectors in 3D space, where the $hati$ unit vector is mapped to

$$
beginbmatrix
1 \
4 \
7 \
endbmatrix
$$

the $hatj$ unit vector is mapped to

$$
beginbmatrix
2 \
5 \
8 \
endbmatrix
$$

and the $hatk$ unit vector is mapped to

$$
beginbmatrix
3 \
6 \
9 \
endbmatrix
$$

So, what does it mean when a matrix consists of functions and not scalars, such as this

$$
beginbmatrix
x & x^2 & x^3 \
y & y^2 & y^3 \
z & z^2 & z^3 \
endbmatrix
$$

What kind of transformation/mapping occurs for the unit vectors?

matrices

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asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

0

$begingroup$

As far as I understand, the matrix

$$
beginbmatrix
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
endbmatrix
$$

refers to a linear transformation of the unit vectors in 3D space, where the $hati$ unit vector is mapped to

$$
beginbmatrix
1 \
4 \
7 \
endbmatrix
$$

the $hatj$ unit vector is mapped to

$$
beginbmatrix
2 \
5 \
8 \
endbmatrix
$$

and the $hatk$ unit vector is mapped to

$$
beginbmatrix
3 \
6 \
9 \
endbmatrix
$$

So, what does it mean when a matrix consists of functions and not scalars, such as this

$$
beginbmatrix
x & x^2 & x^3 \
y & y^2 & y^3 \
z & z^2 & z^3 \
endbmatrix
$$

What kind of transformation/mapping occurs for the unit vectors?

matrices

share|cite|improve this question

asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

As far as I understand, the matrix

$$
beginbmatrix
1 & 2 & 3 \
4 & 5 & 6 \
7 & 8 & 9 \
endbmatrix
$$

refers to a linear transformation of the unit vectors in 3D space, where the $hati$ unit vector is mapped to

$$
beginbmatrix
1 \
4 \
7 \
endbmatrix
$$

the $hatj$ unit vector is mapped to

$$
beginbmatrix
2 \
5 \
8 \
endbmatrix
$$

and the $hatk$ unit vector is mapped to

$$
beginbmatrix
3 \
6 \
9 \
endbmatrix
$$

So, what does it mean when a matrix consists of functions and not scalars, such as this

$$
beginbmatrix
x & x^2 & x^3 \
y & y^2 & y^3 \
z & z^2 & z^3 \
endbmatrix
$$

What kind of transformation/mapping occurs for the unit vectors?

matrices

share|cite|improve this question

asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

lettuceconquerlettuceconquer

11

New contributor

lettuceconquer is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked yesterday

lettuceconquerlettuceconquer

11