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An Introduction to Linear Algebra for Quantum Computing - Qiskit

Last updated Jun 23, 2022

Link URL:: https://learn.qiskit.org/course/ch-appendix/an-introduction-to-linear-algebra-for-quantum-computing

# Notes

$$\begin{align*}\sigma_y \\ = \\ \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \\ \\ \\ \\ \\ \sigma_y^{\dagger} \\ = \\ \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}\end{align*}$$ $$\begin{align*}\sigma_y^{\dagger} \sigma_y \\ = \\ \begin{pmatrix} (0)(0) + (-i)(i) & (0)(-i) \\ + \\ (-i)(0) \\ (i)(0) \\ + \\ (0)(i) & (i)(-i) \\ + \\ (0)(0) \end{pmatrix} \\ = \\ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \\ = \\ \mathbb{I}\end{align*}$$ - Unitary matrices leave the length of a complex vector/ Quantum State unchanged.