Abstract (EN):
Over a general field and for an arbitrary positive integer k, those triangular matrices whose kth power is diagonal are explicitly characterized. This is then used to characterize those complex matrices whose kth power is normal. This gives corresponding results for matrices whose kth power is Hermitian or real symmetric. Our results generalize and imply a recent result about eventually normal and eventually Hermitian matrices.
Language:
English
Type (Professor's evaluation):
Scientific
No. of pages:
10