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Merge pull request #93 from HeroGalak/main
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Update 02_math_recap_linear_algebra.ipynb
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iacopomasi authored Mar 25, 2024
2 parents f84440a + 200f1bf commit fa349c1
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"\n",
"![The matrix $\\mathbf{A}$ again distorting the grid. This time, I want to draw particular attention to what happens to the highlighted square.](https://raw.githubusercontent.com/d2l-ai/d2l-en/master/img/grid-transform-filled.svg)\n",
"\n",
"**Sanity Check:** We cannot apply Pythagoras Theorem to compute area because axes are not aligned anymore.\n",
"**Sanity Check:** We cannot apply Pythagoras Theorem to compute area because axes are not orthogonal anymore.\n",
"\n",
"The picture is misleading since the axis is **CLOSED to be aligned**.\n",
"The picture is misleading since the axis is **CLOSED to be orthogonal**.\n",
"\n",
"The angle between $[1, -1]$ and $[2,3]$ is 101.30993247402021\n",
"The angle between $[1, -1]$ and $[2,3]$ is 101.30993247402021 degrees\n",
"```python import numpy as np; X = np.array([[1, -1], [2, 3]]);thetarad = angle(X[0,:],X[1,:]);theta = thetarad*180/np.pi; print(theta)}}\n",
"```\n",
"\n",
"The angle between $[1, 0]$ and $[0, 1]$ is 90.\n",
"The angle between $[1, 0]$ and $[0, 1]$ is 90 degrees.\n",
"\n",
"```python\n",
"is_basis = False\n",
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