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03_001_Transpose_matrix_Squre_matrix_Diagonal_matrix_Scalar_matrix_Identity_matrix_Symmetry_matrix_Orthogonal_matrix.html
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transpose matrix
2018-06-11 07-53-43.png
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squre matrix
diagonal matrix
2018-06-11 07-54-55.png
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scalar matrix
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identity matrix
2018-06-11 07-56-24.png
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symmetry matrix
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$$$S^{T}=S$$$
orthogonal matrix
2018-06-11 08-05-14.png
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$$$AA^{T}=A^{T}A=I$$$
Let's think of matrix A which is composed of n number of row vectors $$$x_{1}, x_{2}, ..., x_{n}$$$
2018-06-11 07-58-57.png
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$$$(x_{1},x_{1})=x_{1}\cdot x_{1}$$$
$$$0 = x_{1}\cdot x_{2} \rightarrow \cos\theta=0$$$, $$$\theta=90^{\circ}$$$
oneself$$$\cdot$$$ oneself = 1, oneself$$$\cdot$$$ other = 0
In other words, vectors $$$x_{1}, x_{2}, ..., x_{n}$$$ are orthogonal
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