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Then by the Fundamental Theorem of Linear Algebra: 7 ≤ rank(L) ≤ min(dim(L), dim(LT)). With A = null(L) and B = range(L), the matrix representation of L, relative to the decomposition of R^3 = A ⊕ B, is given by:
1. A is a k x k matrix.
2. B is a (-k) x (-k) matrix.
3. D is a (-W) x (-k) matrix.
4. k = rank(L).
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Diagonalize this matrix by constructing its eigenvalue matrix $\Lambda$ and its eigenvector matrix $S$ :$$A=\left[\begin{array}{cc}2 & 1-i \\1+i & 3\end{array}\right]=A^{\mathrm{H}}$$
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