Prove the following identity

the sum running through and the matrix being of size .

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# [Some punny title about determinants and fixed points]

# A two-liner

# Finite codimension

# Still expecting my fix

# Deranged cohomology

# What goes up must come down

# Its hip to be skew

Prove the following identity

the sum running through and the matrix being of size .

Is there a ring such that there are two different ring injections ?

Let be Banach (more generally Fréchet) spaces and let be continuous linear maps. Suppose that is surjective and is compact. Prove that has closed image and .

What’s the expected number of fixed points of a uniformly distributed random permutation of elements?

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Let such that . Prove that .

Show that the determinant of a skew symmetric matrix is never reducible when viewed as a polynomial in variables.