math54-f22:sample_midterm_2
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math54-f22:sample_midterm_2 [2022/11/09 04:20] pzhou |
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| 4. Let $v_1 = (0, 2, 1)$ , $v_2 = (1, 2, 3)$, and $v_3 = (1,1,1)$. Let $V_*$ denote the complete flag associated to $v_i$, namely $V_1 = span(v_1), V_2 = span(v_1, v_2), V_3 = span(v_1, | 4. Let $v_1 = (0, 2, 1)$ , $v_2 = (1, 2, 3)$, and $v_3 = (1,1,1)$. Let $V_*$ denote the complete flag associated to $v_i$, namely $V_1 = span(v_1), V_2 = span(v_1, v_2), V_3 = span(v_1, | ||
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| + | Conceptual | ||
| 5. True or False | 5. True or False | ||
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| * Let $Q_1, Q_2$ be two quadratic form on $\R^n$, is $Q_1 + Q_2$ also a quadratic form? | * Let $Q_1, Q_2$ be two quadratic form on $\R^n$, is $Q_1 + Q_2$ also a quadratic form? | ||
| * Let $Q_1$ be the standard quadratic form on $\R^n$, $Q_2$ be any quadratic form on $\R^n$. Can one find an basis $e_1, \cdots, e_n$ that is orthogonal with respect to both $Q_1, Q_2$? | * Let $Q_1$ be the standard quadratic form on $\R^n$, $Q_2$ be any quadratic form on $\R^n$. Can one find an basis $e_1, \cdots, e_n$ that is orthogonal with respect to both $Q_1, Q_2$? | ||
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| + | ==== Others ===== | ||
| + | For the application of the Sylvester rule, one can refer to the homework question. | ||
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math54-f22/sample_midterm_2.1667967652.txt.gz · Last modified: 2026/02/21 14:44 (external edit)
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