233 lines
3.2 KiB
Markdown
233 lines
3.2 KiB
Markdown
## Matrix
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Matrix(l: list[list[complexe]])
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- l: representation of the matrix in a list
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### Attributes
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- ```__m: list[list[complexe]]```
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the values contained in the matrix.
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- ```__size: tuple[int, int]```
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the size of the matrix
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### Methode
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- ```__init__(l: list[list[complex]]=[]) -> None```
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initiates the matrix
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- ```__mul__(__value: "Matrix") -> Matrix```
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defines the natural multiplication as the Koeneger product for matrices
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- ```__apply(x: list[complex]) -> list[complex]```
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takes a list to represent a vector in a colonne, and return the proctuct of the matrix by this vector
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- ```__str__() -> str```
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returns a string representation of the matrix
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### Staticmethods
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- ```I() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0\\
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0 & 1
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\end{pmatrix}
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```
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- ```H() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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\frac {1} {\sqrt 2} & \frac {1} {\sqrt 2}\\
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\frac {1} {\sqrt 2} & -\frac{1} {\sqrt 2}
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\end{pmatrix}
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```
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- ```X() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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0 & 1\\
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1 & 0
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\end{pmatrix}
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```
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- ```SQRTX() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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\frac {1+i} {2} & \frac {1-i} {2}\\
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\frac {1-i} {2} & \frac {1+i} {2}
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\end{pmatrix}
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```
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- ```Y() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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0 & -i\\
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i & 0
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\end{pmatrix}
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```
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- ```Z() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0\\
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0 & -1
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\end{pmatrix}
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```
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- ```S() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0\\
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0 & i
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\end{pmatrix}
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```
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- ```T() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0\\
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0 & e^{i\frac {\pi} {4}}
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\end{pmatrix}
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```
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- ```Rx(phi: float) -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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\cos(\frac \phi 2) & -i\sin(\frac \phi 2)\\
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-i\sin(\frac \phi 2) & \cos(\frac \phi 2)
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\end{pmatrix}
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```
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- ```Ry(phi: float) -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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\cos(\frac \phi 2) & -\sin(\frac \phi 2)\\
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\sin(\frac \phi 2) & \cos(\frac \phi 2)
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\end{pmatrix}
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```
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- ```Rz(phi: float) -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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e^{-i\frac \phi 2} & 0\\
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0 & e^{i\frac \phi 2}
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\end{pmatrix}
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```
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- ```R1(phi: float) -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & p\\
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0 & e^{i\phi}
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\end{pmatrix}
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```
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- ```CX() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 0 & 1\\
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0 & 0 & 1 & 0
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\end{pmatrix}
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```
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- ```CY() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 0 & -i\\
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0 & 0 & i & 0
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\end{pmatrix}
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```
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- ```CZ() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 1 & 0\\
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0 & 0 & 0 & -1
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\end{pmatrix}
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```
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- ```SWAP() -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 0 & 1 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & 0 & 0
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\end{pmatrix}
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```
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- ```Cu(u: Matrix) -> Matrix```
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returns the matrix
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```math
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\begin{pmatrix}
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1 & 0 & 0 & 0\\
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0 & 1 & 0 & 0\\
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0 & 0 & u_{00} & u_{01}\\
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0 & 0 & u_{10} & u_{11}
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\end{pmatrix}
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```
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