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Bi-Oriented Interlaced Matrix Multiplication and an Operator Factorisation of the Quantum Harmonic Oscillator
We introduce a bi-oriented interlaced matrix product on $2\times 2$ matrices over a unital, possibly non-associative algebra, extending a matrix mnemonic for Cayley--Dickson doubling. The opposite orientations $X_R$ and $X_L$ coincide precisely when the underlying algebra is commutative. For the can
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