線性代數›Ch7 內積空間
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26. Gram-Schmidt、Orthonormal Basis
#LA-07-026中Gram-SchmidtOrthonormal Basis
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The subspace UU of R4\mathbf{R}^4 is spanned by the three vectors: v1=[1,−1,−1,1]T\mathbf{v}_1 = [1, -1, -1, 1]^T, v2=[1,2,−3,2]T\mathbf{v}_2 = [1, 2, -3, 2]^T, v3=[3,3,0,−2]T\mathbf{v}_3 = [3, 3, 0, -2]^T.

Use the Gram-Schmidt process to find the orthonormal basis of UU: t1=[12,−12,−12,12]T\mathbf{t}_1 = \left[\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, \frac{1}{2}\right]^T, t2=[m,n,p,q]T\mathbf{t}_2 = [m, n, p, q]^T, t3=[r,s,x,y]T\mathbf{t}_3 = [r, s, x, y]^T. D=(Round{1n2s2})%5D = \left(\mathrm{Round}\left\{\frac{1}{n^2 s^2}\right\}\right) \% 5. What is DD? (% is the modulo operation. Round{z} rounds z to the nearest integer.)

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