 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2023/digital-systems-linear-algebra-and-introduction-to-formal-proof/6/c/solution

Split

B

B = S \frac{B + B ^{⊤}}{2} + K \frac{B - B ^{⊤}}{2} .

Taking the transpose gives

S^{⊤} = S

and

K^{⊤} = - K

. Thus

S

K

a skew-symmetric matrix. These formulas also show uniqueness, since a real matrix that is both symmetric and skew-symmetric is zero.

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