2. Show that tr(AB) = tr(BA) for any n-square matrices A and B, where tr(AB) and tr(BA) denote the trace of AB and BA, respectively.(7%)

8. Let the probabilities for characters A, B, C, D, E, F to appear in acharacter string be \( \frac{5}{54} \), \( \frac{6}{54} \), \( \frac{7}{54} \), \( \frac{9}{54} \), \( \frac{10}{54} \), and \( \frac{17}{54} \)respectively. Findbinary codes for these characters such that when a characterstring of these characters is represented by your code the binarystring will be of minimal length. Is 010101010101010 a binarystring corresponding to a character string in your code? Describehow do you find the character string of a binary string in yourcode? [10%]

2. Show that \( \text{tr}(AB) = \text{tr}(BA) \) for any \( n \)-square matrices \( A \) and \( B \), where \( \text{tr}(AB) \) and \( \text{tr}(BA) \) denote the trace of \( AB \) and \( BA \), respectively.
(7%)

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相關試卷

2. Show that \( \text{tr}(AB) = \text{tr}(BA) \) for any \( n \)-square matrices \( A \) and \( B \), where \( \text{tr}(AB) \) and \( \text{tr}(BA) \) denote the trace of \( AB \) and \( BA \), respectively.(7%)

相關申論題

相關試卷

2. Show that \( \text{tr}(AB) = \text{tr}(BA) \) for any \( n \)-square matrices \( A \) and \( B \), where \( \text{tr}(AB) \) and \( \text{tr}(BA) \) denote the trace of \( AB \) and \( BA \), respectively.
(7%)