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GR191511
- 76
- 6
I came across a statement in《A First Course in General Relativity》:“The only matrix diagonal in all frames is a multiple of the identity：all its diagonal terms are equal.”Why?I don’t remember this conclusion in linear algebra.The preceding part of this sentence is:Viscosity is a force parallel to the interface between particles.Its absence means that the forces should always be peependicular to the interface,i.e.that ##T^i{^j}####\;## should be zero unless i=j.This means that ##T^i{^j}####\;## should be a diagonal matrix.Moreover,it must be diagonal in all MCRF frame,since“no viscosity”is a statement independent of the spatial axes.(T is stress-energy tensor)