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Matrix (A and A' are equivalent (A and A' are similar (A' is…
Matrix
A and A' are equivalent
A and A' are similar
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A' is diagnolisable
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\[A'= D=S^{-1}AS,
S=[e_1,e_2,e_3,...,e_n]\]
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\[{A'}_{ m \times n}=T_{m \times m }^{-1} \cdot { A_{m \times n}}S_{n \times n}\] \[det(T), det(S) \neq 0\]
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Vectors
scalar/dot product/inner product\[ u \cdot v =||u|| ||v|| cos \theta = \sum_{i=1}^{n}a_i b_i =a^T b = b^T a\]
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\[P^2=P, P_\pi x=p\]
projection matrix, eigenvalues are either 0 or 1, \[P=\frac{bb^T}{||b|||^2 (i.e.b^Tb)}\], b basis bector
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