Multiplication of linear transformation matrices for a combined transformation
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I am new to linear algebra, and I have a rather basic question:
If I know the transformation matrix for linear transformation S ($R^3 to R^3)$ at standard basis E (let's say it is of order 3x3) and I know the transformation matrix for linear transformation T ($R^3 to R^3)$ at standard basis E (let's say it is also of order 3x3); can I then calculate the transformation matrix for the transformation ST at standard basis E by simply multiplying the matrix of S times the matrix of T?
In other words $[ST]_E=[S]_E·[T]_E$?
Thank you!
linear-algebra matrices linear-transformations
asked Dec 31 '18 at 20:15
daltadalta
1578
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add a comment |
$begingroup$
I am new to linear algebra, and I have a rather basic question:
If I know the transformation matrix for linear transformation S ($R^3 to R^3)$ at standard basis E (let's say it is of order 3x3) and I know the transformation matrix for linear transformation T ($R^3 to R^3)$ at standard basis E (let's say it is also of order 3x3); can I then calculate the transformation matrix for the transformation ST at standard basis E by simply multiplying the matrix of S times the matrix of T?
In other words $[ST]_E=[S]_E·[T]_E$?
Thank you!
linear-algebra matrices linear-transformations
asked Dec 31 '18 at 20:15
daltadalta
1578
$endgroup$
2
$begingroup$
You are correct
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– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30
add a comment |
$begingroup$
I am new to linear algebra, and I have a rather basic question:
If I know the transformation matrix for linear transformation S ($R^3 to R^3)$ at standard basis E (let's say it is of order 3x3) and I know the transformation matrix for linear transformation T ($R^3 to R^3)$ at standard basis E (let's say it is also of order 3x3); can I then calculate the transformation matrix for the transformation ST at standard basis E by simply multiplying the matrix of S times the matrix of T?
In other words $[ST]_E=[S]_E·[T]_E$?
Thank you!
linear-algebra matrices linear-transformations
asked Dec 31 '18 at 20:15
daltadalta
1578
$endgroup$
I am new to linear algebra, and I have a rather basic question:
If I know the transformation matrix for linear transformation S ($R^3 to R^3)$ at standard basis E (let's say it is of order 3x3) and I know the transformation matrix for linear transformation T ($R^3 to R^3)$ at standard basis E (let's say it is also of order 3x3); can I then calculate the transformation matrix for the transformation ST at standard basis E by simply multiplying the matrix of S times the matrix of T?
In other words $[ST]_E=[S]_E·[T]_E$?
Thank you!
linear-algebra matrices linear-transformations
linear-algebra matrices linear-transformations
asked Dec 31 '18 at 20:15
daltadalta
1578
asked Dec 31 '18 at 20:15
daltadalta
1578
asked Dec 31 '18 at 20:15
daltadalta
1578
asked Dec 31 '18 at 20:15
daltadalta
1578
asked Dec 31 '18 at 20:15
daltadalta
1578
1578
2
$begingroup$
You are correct
$endgroup$
– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30
add a comment |
2
$begingroup$
You are correct
$endgroup$
– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30
2
2
$begingroup$
You are correct
$endgroup$
– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
You are correct
$endgroup$
– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30
add a comment |
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2
$begingroup$
You are correct
$endgroup$
– Shubham Johri
Dec 31 '18 at 20:23
$begingroup$
@ShubhamJohri Thank you!
$endgroup$
– dalta
Jan 1 at 13:30