MathDB

3

Part of 2005 IMC

Problems(2)

IMC 2005 day 1 pb 3

Source: Peter

7/26/2005
3) ff cont diff, R→]0,+∞[R\rightarrow ]0,+\infty[, prove ∣∫01f3−f(0)2∫01f∣≤max⁡[0,1]∣f′∣(∫01f)2|\int_{0}^{1}f^{3}-{f(0)}^{2}\int_{0}^{1}f| \leq \max_{[0,1]} |f'|(\int_{0}^{1}f)^{2}
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IMC 2005 day 2 pb3

Source: Peter

7/26/2005
What is the maximal dimension of a linear subspace V V of the vector space of real n×n n \times n matrices such that for all A A in B B in V V, we have \text{trace}\left(AB\right) \equal{} 0 ?
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