暑假打發(fā)時(shí)間2

2023-08-03 16:11 作者:臥煙鈴 0人讀過(guò) | 我要投稿

今天本來(lái)打算把文明6拷過(guò)去玩的，拷了半個(gè)小時(shí)沒(méi)有拷下來(lái)就直接過(guò)去了

于是隨便做點(diǎn)題打發(fā)時(shí)間

1.(西南大學(xué))

$%E8%AE%BEA%2CB%E6%98%AFn%E9%98%B6%E5%AE%9E%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%EF%BC%8CC%E6%98%AFn%E9%98%B6%E5%8F%8D%E5%AF%B9%E7%A7%B0%E5%AE%9E%E7%9F%A9%E9%98%B5$

$%E8%8B%A5A%5E2%2BB%5E2%3DC%5E2%2C%E8%AF%81%E6%98%8E%EF%BC%9AA%3DB%3DC%3DO$

$%E8%AF%81%EF%BC%9A$

$A%3DA%5ET%2CB%3DB%5ET%2CC%5ET%3D-C$

$A%3D(a_%7Bij%7D)%2CB%3D(b_%7Bij%7D)%2CC%3D(c_%7Bij%7D)$

$%E6%88%91%E4%BB%AC%E5%AE%B9%E6%98%93%E5%BE%97%E5%88%B0a_%7Bij%7D%3Da_%7Bji%7D%2Cb_%7Bij%7D%3Db_%7Bji%7D$

$%E4%B8%94c_%7Bij%7D%3D-c_%7Bji%7D$

而 $C%5E2%3D%5Cbegin%20%7Bpmatrix%7D%20-(c_%7B11%7D%5E2%2B%5Ccdots%20%2Bc_%7B1n%7D%5E2)%20%26%5Ccdots%20%26%20%5Ccdots%26%5Ccdots%5C%5C%20%5Ccdots%0A%26%20%20-(c_%7B21%7D%5E2%2B%5Ccdots%20%2Bc_%7B2n%7D%5E2)%20%26%20%5Ccdots%26%5Ccdots%20%5C%5C%5Ccdots%0A%26%5Ccdots%20%26%20%5Ccdots%20%26%5Ccdots%20%5C%5C%20%5Ccdots%0A%26%5Ccdots%26%5Ccdots%20%26%20-(c_%7Bn1%7D%5E2%2B%5Ccdots%20%2Bc_%7Bnn%7D%5E2)%20%20%5Cend%7Bpmatrix%7D$

$A%5E2%3D%5Cbegin%20%7Bpmatrix%7D%20(a_%7B11%7D%5E2%2B%5Ccdots%20%2Ba_%7B1n%7D%5E2)%20%26%5Ccdots%20%26%5Ccdots%20%26%5Ccdots%5C%5C%5Ccdots%0A%26%20%20(a_%7B21%7D%5E2%2B%5Ccdots%20%2Ba_%7B2n%7D%5E2)%20%26%5Ccdots%20%26%5Ccdots%20%5C%5C%5Ccdots%0A%26%5Ccdots%20%26%20%5Ccdots%20%26%5Ccdots%20%5C%5C%20%5Ccdots%0A%26%5Ccdots%26%5Ccdots%20%26%20(a_%7Bn1%7D%5E2%2B%5Ccdots%20%2Ba_%7Bnn%7D%5E2)%20%20%5Cend%7Bpmatrix%7D$

$B%5E2%3D%5Cbegin%20%7Bpmatrix%7D%20(b_%7B11%7D%5E2%2B%5Ccdots%20%2Bb_%7B1n%7D%5E2)%20%26%5Ccdots%20%26%5Ccdots%20%26%5Ccdots%5C%5C%5Ccdots%0A%26%20%20(b_%7B21%7D%5E2%2B%5Ccdots%20%2Bb_%7B2n%7D%5E2)%20%26%5Ccdots%20%26%5Ccdots%20%5C%5C%5Ccdots%0A%26%5Ccdots%20%26%20%5Ccdots%20%26%5Ccdots%20%5C%5C%20%5Ccdots%0A%26%5Ccdots%26%5Ccdots%20%26%20(b_%7Bn1%7D%5E2%2B%5Ccdots%20%2Bb_%7Bnn%7D%5E2)%20%20%5Cend%7Bpmatrix%7D$

$%20(b_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bb_%7Bin%7D%5E2)%5Cgeq0%2C%20(a_%7Bi1%7D%5E2%2B%5Ccdots%20%2Ba_%7Bin%7D%5E2)%5Cgeq0%2C%5Cforall%20i%3D1%2C%5Ccdots%2Cn$

$%20-(c_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bc_%7Bin%7D%5E2)%3D%20(b_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bb_%7Bin%7D%5E2)%2B(a_%7Bi1%7D%5E2%2B%5Ccdots%20%2Ba_%7Bin%7D%5E2)$

$%20-(c_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bc_%7Bin%7D%5E2)%5Cleq%200$

$%E4%BA%8E%E6%98%AF%20-(c_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bc_%7Bin%7D%5E2)%3D(b_%7Bi1%7D%5E2%2B%5Ccdots%20%2Bb_%7Bin%7D%5E2)%2B(a_%7Bi1%7D%5E2%2B%5Ccdots%20%2Ba_%7Bin%7D%5E2)%3D0$

$%E4%BA%8E%E6%98%AF%20c_%7Bij%7D%5E2%3Db_%7Bij%7D%5E2%3Da_%7Bij%7D%5E2%3D0%2C%5Cforall%20i%2Cj%3D1%2C%5Ccdots.n$

$%E6%9C%80%E5%90%8EA%3DB%3DC%3DO$

2.(西南大學(xué))

$A%2CB%E4%B8%BAn%E9%98%B6%E5%AE%9E%E6%96%B9%E9%98%B5%EF%BC%8CA%E6%9C%89n%E4%B8%AA%E4%B8%8D%E5%90%8C%E7%89%B9%E5%BE%81%E5%80%BC$

$%E8%8B%A5AB%3DBA%EF%BC%8C%E8%AF%81%E6%98%8E%EF%BC%9A%E5%AD%98%E5%9C%A8%E4%B8%80%E4%B8%AA%E5%A4%9A%E9%A1%B9%E5%BC%8Ff(x)%2C%E4%BD%BF%E5%BE%97B%3Df(A)$

$%E8%AF%81%EF%BC%9A%E2%80%9C%E5%BF%85%E8%A6%81%E6%80%A7%E2%80%9D$

$%E8%AE%BEA%20%E7%9A%84n%E4%B8%AA%E7%89%B9%E5%BE%81%E5%80%BC%E5%88%86%E5%88%AB%E4%B8%BA%5Clambda_1%2C%5Ccdots%2C%5Clambda_n$

$%E5%AD%98%E5%9C%A8%E4%B8%80%E4%B8%AA%E5%8F%AF%E9%80%86n%E9%98%B6%E6%96%B9%E9%98%B5P%E4%BD%BF%E5%BE%97$

$A%3DP%5Cbegin%20%7Bpmatrix%7D%20%5Clambda_1%20%26%20%26%20%26%5C%5C%5C%0A%26%20%5Clambda_2%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26%20%5Clambda_n%20%20%5Cend%7Bpmatrix%7DP%5E%7B-1%7D%3DP%5CLambda_aP%5E%7B-1%7D$

$%E8%8B%A5%E5%AD%98%E5%9C%A8%E4%B8%80%E4%B8%AA%E5%A4%9A%E9%A1%B9%E5%BC%8Ff(x)%2C%E4%BD%BF%E5%BE%97B%3Df(A)$

$%E5%88%99B%3Df(A)%3DPf(%5Cbegin%20%7Bpmatrix%7D%20%5Clambda_1%20%26%20%26%20%26%5C%5C%5C%0A%26%20%5Clambda_2%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26%20%5Clambda_n%20%20%5Cend%7Bpmatrix%7D)P%5E%7B-1%7D%3DP%5Cbegin%20%7Bpmatrix%7Df(%20%5Clambda_1)%20%26%20%26%20%26%5C%5C%5C%0A%26f(%20%5Clambda_2)%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26f(%20%5Clambda_n)%20%20%5Cend%7Bpmatrix%7DP%5E%7B-1%7D$

$%E5%88%99B%3DP%5Cbegin%20%7Bpmatrix%7Df(%20%5Clambda_1)%20%26%20%26%20%26%5C%5C%5C%0A%26f(%20%5Clambda_2)%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26f(%20%5Clambda_n)%20%20%5Cend%7Bpmatrix%7DP%5E%7B-1%7D%3DP%5CLambda_bP%5E%7B-1%7D$

$%E5%88%99AB%3DP%5CLambda_aP%5E%7B-1%7DP%5CLambda_bP%5E%7B-1%7D%3DP%5CLambda_a%5CLambda_bP%5E%7B-1%7D$

$%E8%80%8C%5CLambda_a%2C%5CLambda_b%E9%83%BD%E6%98%AF%E5%AF%B9%E8%A7%92%E9%98%B5AB%3DP%5CLambda_a%5CLambda_bP%5E%7B-1%7D%3DP%5CLambda_b%5CLambda_aP%5E%7B-1%7D%3DBA$

$%E2%80%9C%E5%85%85%E5%88%86%E6%80%A7%E2%80%9D$

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$%E8%AE%BEB%E7%9A%84n%E4%B8%AA%E7%89%B9%E5%BE%81%E5%80%BC%E5%88%86%E5%88%AB%E4%B8%BA%5Cmu_1%2C%5Ccdots%2C%5Cmu_n$

$%E5%AD%98%E5%9C%A8%E4%B8%80%E4%B8%AA%E5%8F%AF%E9%80%86n%E9%98%B6%E6%96%B9%E9%98%B5Q%E4%BD%BF%E5%BE%97$

$B%3DQ%5Cbegin%20%7Bpmatrix%7D%20%5Clambda_1%20%26%20%26%20%26%5C%5C%5C%0A%26%20%5Clambda_2%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26%20%5Clambda_n%20%20%5Cend%7Bpmatrix%7DQ%5E%7B-1%7D%3DQ%5CLambda_bQ%5E%7B-1%7D$

$%E8%8B%A5AB%3DBA%2C%E5%88%99P%5CLambda_aP%5E%7B-1%7DQ%5CLambda_bQ%5E%7B-1%7D%3DQ%5CLambda_bQ%5E%7B-1%7DP%5CLambda_aP%5E%7B-1%7D$

$%E5%88%99%5CLambda_aP%5E%7B-1%7DQ%5CLambda_bQ%5E%7B-1%7DP%3DP%5E%7B-1%7DQ%5CLambda_bQ%5E%7B-1%7DP%5CLambda_a$

$P%5E%7B-1%7DQ%5CLambda_bQ%5E%7B-1%7DP%3DS%2C%E5%88%99%5CLambda_aS%3DS%5CLambda_a$

$%E8%AE%BES%3D(s_%7Bij%7D)%EF%BC%8C%5CLambda_aS%3DS%5CLambda_a%E5%88%99%E6%8E%A8%E5%87%BA$

$%E5%88%99%E6%8E%A8%E5%87%BA%5Clambda_i%20s_%7Bij%7D%3D%5Clambda_j%20s_%7Bij%7D%2C%E5%8F%88%E5%9B%A0%E4%B8%BA%5Cforall%20i%5Cneq%20j%20%E6%9C%89%5Clambda_i%5Cneq%20%5Clambda_j$

$%5Cforall%20i%5Cneq%20j%20%E6%9C%89s_%7Bij%7D%3D0%2C%E6%89%80%E4%BB%A5S%E6%98%AF%E5%AF%B9%E8%A7%92%E9%98%B5$

$P%5E%7B-1%7DQ%5CLambda_bQ%5E%7B-1%7DP%3DS%E6%98%AF%E5%AF%B9%E8%A7%92%E9%98%B5%EF%BC%8C%E4%B8%94%5CLambda_b%E6%98%AF%E5%AF%B9%E8%A7%92%E9%98%B5$

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$(s_%7Bii%7D%20m_%7Bi1%7D%2Cs_%7Bii%7Dm_%7Bi2%7D%2C%5Ccdots%2Cs_%7Bii%7Dm_%7Bin%7D)%3D(%5Cmu_1m_%7Bi1%7D%2C%5Cmu_2m_%7Bi2%7D%2C%5Ccdots%5Cmu_nm_%7Bin%7D)$

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$%5Cforall%20i%5Cneq%20j%20%E6%9C%89m_%7Bij%7D%3D0%2C%E6%89%80%E4%BB%A5M%E6%98%AF%E5%AF%B9%E8%A7%92%E9%98%B5$

$%E8%8B%A5AB%3DBA%2C%E5%88%99P%5E%7B-1%7DQ%3DM%E4%B8%BA%E5%AF%B9%E8%A7%92%E9%98%B5$

$Q%3DPM%2CB%3DPM%5CLambda_bM%5E%7B-1%7DP%5E%7B-1%7D%3DP%5CLambda_bP%5E%7B-1%7D$

$%E8%8B%A5%E5%AD%98%E5%9C%A8%E4%B8%80%E4%B8%AA%E5%A4%9A%E9%A1%B9%E5%BC%8Ff(x)%2C%E4%BD%BF%E5%BE%97B%3Df(A)$ $%E5%88%99B%3Df(A)%3DPf(%5Cbegin%20%7Bpmatrix%7D%20%5Clambda_1%20%26%20%26%20%26%5C%5C%5C%0A%26%20%5Clambda_2%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26%20%5Clambda_n%20%20%5Cend%7Bpmatrix%7D)P%5E%7B-1%7D%3DP%5Cbegin%20%7Bpmatrix%7Df(%20%5Clambda_1)%20%26%20%26%20%26%5C%5C%5C%0A%26f(%20%5Clambda_2)%20%26%5C%20%26%5C%5C%5C%0A%26%26%20%5Ccdots%20%26%5C%5C%0A%26%26%26f(%20%5Clambda_n)%20%20%5Cend%7Bpmatrix%7DP%5E%7B-1%7D$

$%E4%BA%8E%E6%98%AFf(%5Clambda_i)%3D%5Cmu_i%2C%5Cforall%20i%3D1%2C%5Ccdots%2Cn$

$%E8%AE%BEf(x)%3Da_0%2Ba_1x%2B%5Ccdots%2Ba_%7Bn-1%7Dx%5E%7Bn-1%7D$

$f(%5Clambda_i)%3D%5Cmu_i%2C%5Cforall%20i%3D1%2C%5Ccdots%2Cn%E4%BA%8E%E6%98%AF%E5%BE%97%E5%88%B0$

$%5Cbegin%20%7Bpmatrix%7D%201%20%26%5Clambda_1%20%26%5Ccdots%20%26%5Clambda_1%5E%7Bn-1%7D%5C%5C%5C%201%0A%26%20%5Clambda_2%20%26%5Ccdots%20%26%5Clambda_2%5E%7Bn-1%7D%5C%5C%5Cvdots%0A%26%5Cvdots%26%20%5Cvdots%20%26%5Cvdots%5C%5C%201%20%0A%26%20%5Clambda_n%20%20%26%5Ccdots%26%20%5Clambda_n%5E%7Bn-1%7D%20%20%5Cend%7Bpmatrix%7D%5Cbegin%20%7Bpmatrix%7Da_0%5C%5Ca_1%5C%5C%20%5Cvdots%20%5C%5C%20a_%7Bn-1%7D%5Cend%7Bpmatrix%7D%3D%5Cbegin%20%7Bpmatrix%7D%5Cmu_1%5C%5C%5Cmu_2%5C%5C%20%5Cvdots%20%5C%5C%20%5Cmu_%7Bn%7D%5Cend%7Bpmatrix%7D$