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# Tag Archives: matrices

## Something I didn’t know

I didn’t know this, though probably I should have. Maybe you didn’t know it either. We work in a semigroup, a system with an operation (called multiplication) satisfying the associative law. A generalised inverse of an element A is an … Continue reading

Posted in exposition
Tagged associative law, commute, generalised inverse, matrices, polynomial
4 Comments

## Normal

There are various overused terms in mathematics. “Normal” is one of them. Perhaps the four commonest uses are the following: A complex square matrix is normal if it commutes with its conjugate transpose. Normal matrices are precisely the ones which … Continue reading

Posted in exposition
Tagged Cayley graphs, field extensions, groups, matrices, terminology, topological spaces
3 Comments

## A matrix problem

Suppose you are given n linearly independent vectors in n-dimensional Euclidean space. You move the vectors so that each vector becomes longer, but their inner products remain the same. What happens to the volume of the parallelepiped they span? This … Continue reading

Posted in open problems
Tagged conference matrix, Dennis Lin, determinant, Hadamard matrix, Isaac Newton Institute, matrices, skew-symmetric, statistics
7 Comments