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Zheyuan Wu
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content/Math401/Math401_T2.md
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# Topic 2: Finite-dimensional Hilbert spaces
# Math401 Topic 2: Finite-dimensional Hilbert spaces
Recall the complex number is a tuple of two real numbers, $z=(a,b)$ with addition and multiplication defined by
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The inner product is the standard Hermitian inner product in $\mathbb{C}^{n\times n}$.
#### Definition of Hilbert-Schmidt norm
#### Definition of Hilbert-Schmidt norm (also called Frobenius norm)
The Hilbert-Schmidt norm of a linear operator $T: \mathscr{H}\to \mathscr{H}$ is defined by