資料紹介
Introduction.
A linear transformation, T, of the plane which maps the point P (x, y) onto the point P’ (x’, y’) is defined by the equations...
First, it’s easy to think about so make it the coordinate of OABC as same as Part 1’s b).
Which is O = (0, 0), A = (1, 0), B = (1, 1), C = (0, 1).
To find the transformation of unit square, do the same thing as Part 1, simply substitute the
coordinate into equation.
T1 (x, y) = (-x, y), T2 (x, y) = (y, -x) and T3 (x, y) = (y, x).
and we can get…
For Transformation T1,
T1 (0, 0) = (-x, y) → T1 (0, 0) = (– 0, 0) → O’ (0, 0)
T1 (1, 0) = (-x, y) → T1 (1, 0) = (–1, 0) ..→ A’ (-1, 0)
T1 (1, 1) = (-x, y) → T1 (1, 1) = (–1, 1) ..→ B’, (-1, 1)
T1 (0, 1) = (-x, y) → T1 (0, 1) = (–0, 1) ..→ C’ (0, 1)
From this transformation, we can see that the unit square O’A’B’C’ is image of OABC’s symmetry of the y-axis.
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Transformations and Their Matrices.
Introduction.
A linear transformation, T, of the plane which maps the point P (x, y) onto the point P' (x', y') is defined by the equations;
We also can write transformation as a matrix way.
If we rewrite T (x, y) = (ax + by, cx + dy) = (x', y') in a matrix way, we can write as
If we solve this, we can get transformation matrix T as,
So, if we substitute this matrix into above matrix, we can get
Part 1.
For the linear transformation T0 (x, y) = (2x y, x...
