- #1

- 190

- 1

The matrix is

| 1/2 -1/2 |

| 1/2 1/2 |

Why is this matrix not representing a rotation?

The form of rotation is

| cos x -sin x |

|sin x cos x |

So in this case tan x = 1 and so x = 45...isn't this rotation of 45 degrees?

On similar note, for the matrix

| 5 6 |

| -6 5 |

it says it is a rotation of [itex]\theta[/itex] = arctan (-6/5), which I assumed was obtained by saying that cos x = 5 and sin x = -6 so tan x = -6/5....so what is the difference between this example and my problem?

edit: for the second example, it actually states that this matrix is a rotation combined with scaling. Is this the main reason why the first problem can't be considered just rotation? Because it is actually also scaled? I mean that the rotation formula I gave was derived using the unit vectors, but the vectors represented by the first problem are not unit because their length is 1/2 not 1....? Idk this seems like trivial difference though..

| 1/2 -1/2 |

| 1/2 1/2 |

Why is this matrix not representing a rotation?

The form of rotation is

| cos x -sin x |

|sin x cos x |

So in this case tan x = 1 and so x = 45...isn't this rotation of 45 degrees?

On similar note, for the matrix

| 5 6 |

| -6 5 |

it says it is a rotation of [itex]\theta[/itex] = arctan (-6/5), which I assumed was obtained by saying that cos x = 5 and sin x = -6 so tan x = -6/5....so what is the difference between this example and my problem?

edit: for the second example, it actually states that this matrix is a rotation combined with scaling. Is this the main reason why the first problem can't be considered just rotation? Because it is actually also scaled? I mean that the rotation formula I gave was derived using the unit vectors, but the vectors represented by the first problem are not unit because their length is 1/2 not 1....? Idk this seems like trivial difference though..

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