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Geometric meaning of a matrix

How do I describe the geometric meaning of the 2x2 matrix
1 -1
1 1
Reply 1
Avatar for Zacken
Zacken
22
Original post by Balkaran
How do I describe the geometric meaning of the 2x2 matrix
1 -1
1 1


What does it do to the (standard) basis vectors of R^2? That might help you see what transformation it represents.
Reply 2
Avatar for Balkaran
Balkaran
OP
10
Original post by Zacken
What does it do to the (standard) basis vectors of R^2? That might help you see what transformation it represents.


I'm confused with what you mean.
what is the standard basis vectors is it the identity matrix?
Reply 3
Avatar for B_9710
B_9710
18
You should be able to identify that it's of a standard form of a type of transformation matrix.
Reply 4
Avatar for Zacken
Zacken
22
Original post by Balkaran
I'm confused with what you mean.
what is the standard basis vectors is it the identity matrix?


e_1 = (1 0) and e_2 = (0 1)
Original post by Balkaran
How do I describe the geometric meaning of the 2x2 matrix
1 -1
1 1


I would use the base vectors which are
1
0

and

0
1

Multiply the matrix by each of those to see what happens to a unit square..
Reply 6
Avatar for Balkaran
Balkaran
OP
10
Original post by B_9710
You should be able to identify that it's of a standard form of a type of transformation matrix.


what's a standard form of a matrix
Reply 7
Avatar for B_9710
B_9710
18
Original post by Balkaran
what's a standard form of a matrix


Never mind what I said I didn't even read the matrix correctly
Reply 8
Avatar for Balkaran
Balkaran
OP
10
Original post by Muttley79
I would use the base vectors which are
1
0

and

0
1

Multiply the matrix by each of those to see what happens to a unit square..


yeah I did that the image I got
0 1 0 -1
0 1 2 1
Reply 9
Avatar for Balkaran
Balkaran
OP
10
Original post by Zacken
e_1 = (1 0) and e_2 = (0 1)


wait is it a rotation then enlargement because it enlarges by root(2) cause the det is 2 and looks like it rotates by 45 degrees

I'm not sure
(edited 6 years ago)
Reply 10
Avatar for Zacken
Zacken
22
Original post by Balkaran
wait is it a rotation then enlargement because it enlarges by root(2) cause the det is 2 and looks like it rotates by 45 degrees

I'm not sure


yep

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