If X^{T}\cdot A \cdot X = 0 for some X,

misangela4gi

misangela4gi

Answered question

2022-04-22

If XTAX=0 for some X, what is the condition must impose to A?

Answer & Explanation

haarplukxjf

haarplukxjf

Beginner2022-04-23Added 16 answers

Step 1
Guess you mean x as a vector, A being a skew symmetric matrix would be sufficient for all x to make xTAx=0 as the expression xTAx is actually ΣinΣjnAijxixj,
for general case, the condition of A depends on x, like when x is the column vector with all entries equals 1, A need to be the matrix for which all of this entries sum up to 0.

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