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README.md

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A linear transformation is a function from one vector space to another that respects the linear structure of each vector space ([Learn more](https://brilliant.org/wiki/linear-transformations/)). For visualizing this we can transform a vector as we can see in the Fig. 1.
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<figure>
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<img src="https://i.ibb.co/VTRy5Tx/vector-linear-Transformation.png" alt="vector transformed" style="width:40%;
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display: block;
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margin-left: auto;
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margin-right: auto;">
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<figcaption style="text-align: center;">Fig.1 - Vector transformed with a transformation matrix</figcaption>
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</figure>
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<img src="https://i.ibb.co/VTRy5Tx/vector-linear-Transformation.png" width = 400px height = 270px alt="vector transformed">
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<figcaption>Fig.1 - Vector transformed with a transformation matrix</figcaption>
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</figure> </br>
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But it has an obvious problem, because the linear transformation transform the whole space, not just the vector, in other words it transforms the basis vectors thus every vector in the space gets transformed too. That's why i created this app so everyone can see how a transformation matrix change the whole space.
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## How to use
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When you open the app you can see the grid at the left, and the interface at the right. The grid was plotted with color so you can notice the transformations.
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<figure>
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<img src="https://i.ibb.co/NVGsQKw/main-window.png" width = 508px height = 288px alt="vector transformed">
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</figure> </br>
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At the right you can choose an example from the list and it will transform the original grid by the transformation that you have choose from the examples list, remember that the app can't remember the posterior state, so you can't for example rotate the plot 45º in X and then rotate it again 45º in Y, when you do the second transformation it will transform the *original* grid not the grid you got in the first transformation. You can create any transformation matrix and write it in the app and see how it transforms the grid too.
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<figure>
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<img src="https://i.ibb.co/n3PY8sd/examples.png" width = 1016px height = 288px alt="vector transformed">
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</figure> </br>

icon.png

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main.py

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from numpy import linspace,column_stack,array #For create the linspace for the plotting
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import PyQt5.QtWidgets as QtWidgets #Python GUI
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from PyQt5.QtGui import QFont #Pyqt5 fonts
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from PyQt5.QtGui import QFont,QIcon #Pyqt5 fonts
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from Plotting import PlotWidget #The plot object
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[interface.matrix02.text(), interface.matrix12.text(), interface.matrix22.text()]]))
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plot.show()
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app.setWindowIcon(QIcon('icon.png'))
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app.exec()

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