Solving Rotation Matrices Urgently: cos(pi/4) -sin(pi/4) sin(pi/4) cos(pi/4)

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SUMMARY

The discussion focuses on the application of rotation matrices, specifically the matrix for a rotation of pi/4 radians, represented as cos(pi/4) -sin(pi/4) and sin(pi/4) cos(pi/4). The user seeks clarification on extending this concept to a matrix that not only rotates a vector but also doubles its length. The response emphasizes the need for a different matrix that achieves this transformation, indicating a deeper exploration of matrix operations is required.

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  • Understanding of rotation matrices in linear algebra
  • Familiarity with trigonometric functions, particularly cosine and sine
  • Knowledge of matrix multiplication and transformations
  • Basic concepts of vector length and scaling
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  • Research the properties of scaling matrices in linear algebra
  • Learn about the combination of rotation and scaling transformations
  • Explore the derivation of transformation matrices for specific angles
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Students studying linear algebra, mathematicians interested in matrix transformations, and computer graphics developers working with vector manipulations.

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[URGENT] Rotation Matrices

Homework Statement



http://e.imagehost.org/0661/Screen_shot_2010-03-09_at_12_37_44_AM.png

Homework Equations



Rotation Matrix:
cos(theta) -sin(theta)
sin(theta) cos(theta)

The Attempt at a Solution



I understand 2a:

cos(pi/4) -sin(pi/4)
sin(pi/4) cos(pi/4)

But I am not sure what 2b is looking for. Please help?

Thank you in advance for your help!
 
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The matrix you wrote is a rotation matrix, which rotates a vector but leaves its length unchanged. You need a matrix which doubles the length as well. Try to find such one. ehild
 
Last edited:

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