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https://texercises.com/exercise/metrik-tensor-transformieren/
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Exercise:
Gegeben sei der Metrik-Tensor mqty & & im Koordinatensystem mqtye_x & e_y. Wie sieht er im Koordinatensystem mqtytilde e_x & tilde e_y aus falls dieses System über die Transformation mqtytilde e_x & tilde e_y mqtye_x & e_y mqty & & aus dem ersten System hervorgeht?

Solution:
mqtytilde g_xx & tilde g_xy tilde g_yx & tilde g_yy mqtya & b c & d^T mqtyg_xx & g_xy g_yx & g_yy mqtya & b c & d mqty & & ^T mqty & & mqty & & mqty & & mqty & & mqty & &
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\(\LaTeX\)-Code
Exercise:
Gegeben sei der Metrik-Tensor mqty & & im Koordinatensystem mqtye_x & e_y. Wie sieht er im Koordinatensystem mqtytilde e_x & tilde e_y aus falls dieses System über die Transformation mqtytilde e_x & tilde e_y mqtye_x & e_y mqty & & aus dem ersten System hervorgeht?

Solution:
mqtytilde g_xx & tilde g_xy tilde g_yx & tilde g_yy mqtya & b c & d^T mqtyg_xx & g_xy g_yx & g_yy mqtya & b c & d mqty & & ^T mqty & & mqty & & mqty & & mqty & & mqty & &
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Tags
einstein, koordinatentransformation, lineare algebra, mathematik, matrix, metrik, physik, relativ, relativitätstheorie, srt, transformation, transponiert
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(1, default)
Points
3 (default)
Language
GER (Deutsch)
Type
Calculative / Quantity
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Link