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enter image description here

How can it change this to that?

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closed as off-topic by Aaron Stevens, tpg2114 Oct 5 at 14:42

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The first thing to know is how to do matrix multiplication, in your case for example: $$\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} \begin{bmatrix} 1 \\ 0 \end{bmatrix} =\begin{bmatrix} 1 \\ 1 \end{bmatrix}$$

The second thing to know is the convention for ket vectors: $$ \begin{bmatrix} 1 \\ 0 \end{bmatrix} = |0\rangle \quad \begin{bmatrix} 0 \\ 1 \end{bmatrix} = |1\rangle $$

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  • $\begingroup$ thank you very much $\endgroup$ – 134540 Oct 5 at 10:53

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