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Linear AlgebraSuperchallengeOrthogonality & Least Squares

Orthogonality & Least Squares · Superchallenge problem

Find the maximum of x1+2x2+3x3+4x4x_1 + 2x_2 + 3x_3 + 4x_4 over real numbers satisfying x1+x2+x3+x4=0x_1 + x_2 + x_3 + x_4 = 0, x1−x2+x3−x4=0x_1 - x_2 + x_3 - x_4 = 0, and x12+x22+x32+x42=1x_1^2 + x_2^2 + x_3^2 + x_4^2 = 1.