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kumpel [21]
3 years ago
9

What is an idempotent matrix?

Mathematics
2 answers:
Yuki888 [10]3 years ago
7 0
An\ idempotent\ matrix\ is\ a\ matrix\ n\times n\ (square\ matrix\ A)\ which:A^2=A\\\\Example:\\  A=\left[\begin{array}{ccc}2&-1\\2&-1\end{array}\right]\\A^2=\left[\begin{array}{ccc}2&-1\\2&-1\end{array}\right]\cdot\left[\begin{array}{ccc}2&-1\\2&-1\end{array}\right]=\left[\begin{array}{ccc}2\cdot2-1\cdot2&2\cdot(-1)-1\cdot(-1)\\2\cdot2-1\cdot2&2\cdot(-1)-1\cdot(-1)\end{array}\right]\\=  \left[\begin{array}{ccc}4-2&-2+1\\4-2&-2+1\end{array}\right] =  \left[\begin{array}{ccc}2&-1\\2&-1\end{array}\right] =A


Fofino [41]3 years ago
7 0
A matrix E satisfying the equation E2 = E.
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