Matrix

👨🏻‍🏫 學術台數學

yau

2009-09-12 11:15 pm

A is the matrix representing the rotation in the Cartesian plane anticlockwise about the orign by X .

Then , we have A = (cosX -sinX)
-------------------------(sinX cosX)
我想問
Let A be the matrix representing the rotation in the Cartesian plane clockwise about the orign by X .

A still = (cosX -sinX)
-----------(sinX cosX )

更新1:

A still = (cosX -sinX) -----------(sinX cosX ) ???

回答 (1)

用戶9112

2009-09-12 11:50 pm

✔ 最佳答案

You should be able to realise that rotating clockwise by angle X just means rotating anti-clockwise by angle - X. Therefore you can obtain the matrix by substituting -X instead of X in the orginal matrix.
Since cos(-X) = cosX and sin(-X) = -sinX
so the new matrix should be
(cosX sinX)
(-sinX cosX)
Indeed the new matrix is the inverse of A.

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