I'm studying on the following problem. I have a set of four vectors such as v1 = (2, −1, −1, −1), v2 = (−2, 1, 1, 0), v3 = (1, −1, 1, −1), v4 = (1, −2, −2, 2). What I want is finding an orthonormal basis without using Gram-Schmidt orthonormalization method. Is there any way to solve this without using Gram-Schmidt method? Can you please show me a way to solve it? Any help would be appreciated.
2026-03-26 17:46:12.1774547172
Finding an orthonormal basis for the set of vectors.
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Since your vectors are linearly independent they span the four dimensional space $\mathbb {R^4} $ so the standard orthonormal basis $$\{ (1,0,0,0), (0,1, 0,0),(0,0,1,0), (0,0,0,1)\}$$ will do.