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

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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

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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 , , , , , , , | 7 Comments