Chapter 7- Linear transformations Flashcards

1
Q

Linear transformation properties

A

Maps origin onto itself
Representable by a matrix

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2
Q

Reflection in y axis

A

(-1 0)
(0 1)

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3
Q

Reflection in x axis

A

(1 0)
(0 -1)

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4
Q

Reflection y=x

A

(0 1)
(1 0)

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5
Q

Reflection in y=-x

A

(0 -1)
(-1 0)

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6
Q

Rotation angle θ anticlockwise about origin

A

(cosθ -sinθ)
(sinθ cosθ)

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7
Q

Stretch of scale factor a along x axis and stretch of scale factor b along y axis

A

(a 0)
(0 b)

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8
Q

What does detM for a matrix representing a linear transformation show?

A

The area scale factor

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9
Q

Reflection in x=0 plane

A

(-1 0 0)
(0 1 0)
(0 0 1)

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10
Q

Reflection in y=0 plane

A

(1 0 0)
(0 -1 0)
(0 0 1)

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11
Q

Reflection in z=0 plane

A

(1 0 0)
(0 1 0)
(0 0 -1)

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12
Q

Rotation by θ about x axis

A

(1 0 0)
(0 cosθ -sinθ)
(0 sinθ cosθ)

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13
Q

Rotation by θ about y axis

A

(cosθ 0 sinθ)
(0 1 0 )
(-sinθ 0 cosθ)

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14
Q

Rotation by θ about z axis

A

(cosθ -sinθ 0)
(sinθ cosθ 0)
(0 0 1)

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