The nonreal eigenvalues of a real matrix occur in complex conjugate pairs.

Tuesday, September 20, 2016 Trigonometry, Week 4 2.2: Period, Phase Shift, and Other Translations Period Change - horizontal shrink: when you multiply x by a number |B| > 1 - horizontal stretch: when you multiply x by a number |B| < 1 Combining Period and Amplitude Changes - kπ/4 Translations - Vertical Shift: |D| - Vertical Shift Up: D > 0 - Vertical Shift Down: D < 0 - Phase Shift: |C| - Phase Shift Right: C > 0 - Phase Shift Left: C < 0 Effects of A, B, C and D on the graphs of y = cos x & sin x - Amplitude = |A| • |A| > 1 Vert Stretch • |A| < 1 Vert Shrink • A < 0 reﬂection across x axis - Period = |B| • |B| > 1 Horiz Shrink • |B| < 1 Horiz Stretch - Phase Shift = |C| • C > 0 Shift