The real forms of a given complex semisimple Lie algebra are frequently labeled by the positive index of inertia of their Killing form.
2.
These invariants must satisfy some compatibility conditions : a parity relation ( the sign of the discriminant must match the negative index of inertia ) and a product formula ( a local global relation ).
3.
If the matrix " A " has the property that every principal upper left minor " ? " " k " is non-zero then the negative index of inertia is equal to the number of sign changes in the sequence
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