Paper 1, Section I, C

Vectors and Matrices | Part IA, 2016

Write down the general form of a 2×22 \times 2 rotation matrix. Let RR be a real 2×22 \times 2 matrix with positive determinant such that Rx=x|R \mathbf{x}|=|\mathbf{x}| for all xR2\mathbf{x} \in \mathbb{R}^{2}. Show that RR is a rotation matrix.


J=(0110)J=\left(\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right)

Show that any real 2×22 \times 2 matrix AA which satisfies AJ=JAA J=J A can be written as A=λRA=\lambda R, where λ\lambda is a real number and RR is a rotation matrix.

Typos? Please submit corrections to this page on GitHub.