- 1,0.4406197005382-1.56961032189i,0.4406197005382+1.56961032189i,-1.8812394010764
- 矩陣
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
- \begin{bmatrix}{3} & {6} & {9} \\
{9} & {12} & {15} \\
{15} & {18} & {21} \\
{21} & {24} & {27}\end{bmatrix}
- {{29,32,35,38},{65,72,79,86},{101,112,123,134}}
![{\displaystyle {{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {\begin{bmatrix}{7}&{8}&{9}&{10}\\{11}&{12}&{13}&{14}\end{bmatrix}}}={\begin{bmatrix}{29}&{32}&{35}&{38}\\{65}&{72}&{79}&{86}\\{101}&{112}&{123}&{134}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97c32e82d6fadbf213465dc80c2fe599d6f4747c)
![{\displaystyle rows\left({{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {\begin{bmatrix}{7}&{8}&{9}&{10}\\{11}&{12}&{13}&{14}\end{bmatrix}}}\right)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b805431cd1ba78a6d1e00e9417ac0eff76a57200)
- {{3,6},{9,12},{15,18}}
![{\displaystyle {{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {3}}={\begin{bmatrix}{3}&{6}\\{9}&{12}\\{15}&{18}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ba10756e1330d58f7244e28319044fa883d3149)
- {{1,3,5},{2,4,6}}
![{\displaystyle {\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}^{\mathrm {T} }={\begin{bmatrix}{1}&{3}&{5}\\{2}&{4}&{6}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7d48373d77bfb17f3599378766728f4db48c8e5)
![{\displaystyle I_{3}={\begin{bmatrix}{1}&{0}&{0}\\{0}&{1}&{0}\\{0}&{0}&{1}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3ef513776221ce8067296dd43ddd13fa38110ad8)
![{\displaystyle \operatorname {diag} \left(1,\,2,\,3\right)={\begin{bmatrix}{1}&{0}&{0}\\{0}&{2}&{0}\\{0}&{0}&{3}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c49d4d9d2756b4ae241470011f92b06104ec9196)
![{\displaystyle {{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {i}}={\begin{bmatrix}{i}&{2i}\\{3i}&{4i}\\{5i}&{6i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/71828bf4df6e9398135bdbfec116b3c4e95a7c6a)
![{\displaystyle selectlist\left(2,\,3,\,{\begin{bmatrix}{7}&{8}&{9}\\{10}&{11}&{12}\\{13}&{14}&{15}\end{bmatrix}}\right)=12}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9e2097f4de2166bbcdb485118aade000abe35f30)
![{\displaystyle {{{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\times {\begin{bmatrix}{7}&{8}&{9}&{10}\\{11}&{12}&{13}&{14}\end{bmatrix}}}\times {4}}={\begin{bmatrix}{116}&{128}&{140}&{152}\\{260}&{288}&{316}&{344}\\{404}&{448}&{492}&{536}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/410045901066e22ed8ba2289911c3fb632192240)
![{\displaystyle \operatorname {trunc} \left({\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}^{-1},\,5\right)={\begin{bmatrix}{-0.48809}&{-1.21428}&{1.03571}&{0.15476}\\{-0.13095}&{1.35714}&{-0.89285}&{-0.20238}\\{0.58333}&{-0.5}&{0.25}&{0.08333}\\{-0.07142}&{0.28571}&{-0.21428}&{0.07142}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c384d023fce56c94efbaa29498469f564142174f)
![{\displaystyle \det {\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}=-84}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e093ddd57964f7ca8bbc21fc1275ce7f65038f8a)
囧rz……
![{\displaystyle \operatorname {trunc} \left({{\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}\,{{\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}^{-1}}},\,8\right)={\begin{bmatrix}{0.99999999}&{0}&{0}&{0}\\{0}&{1}&{0}&{0}\\{0}&{0}&{1}&{0}\\{0}&{0}&{0}&{0.99999999}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/04e71921084b870743e54a1f72e4b64d700707d4)
![{\displaystyle \mathrm {cof} {\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}={\begin{bmatrix}{41}&{11}&{-49}&{6}\\{102}&{-114}&{42}&{-24}\\{-87}&{75}&{-21}&{18}\\{-13}&{17}&{-7}&{-6}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e418e78f0b2de6e744be49c5162e84bf953b9ee2)
![{\displaystyle \det \left(\mathrm {cof} {\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}\right)_{{2},\,{3}}=-42}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a38367fe72275cc5ed8b8f93fd040bf2b18d9b0a)
![{\displaystyle \operatorname {adj} {\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}={\begin{bmatrix}{41}&{102}&{-87}&{-13}\\{11}&{-114}&{75}&{17}\\{-49}&{42}&{-21}&{-7}\\{6}&{-24}&{18}&{-6}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fd0106f4b204f341de694728e5481a3f816e6522)
![{\displaystyle GaussElimination\left({\begin{bmatrix}{1}&{2}&{3}&{0}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}\right)={\begin{bmatrix}{7}&{9}&{8}&{1}\\{0}&{-1.5714285714286}&{0.71428571428571}&{8.7142857142857}\\{0}&{0}&{2.1818181818182}&{3.8181818181818}\\{0}&{0}&{0}&{3.5}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3222c6b155b01fae2621c86fe45a2ff0f217d2c3)
![{\displaystyle {{\begin{bmatrix}{1}&{2}\\{3}&{4}\\{5}&{6}\end{bmatrix}}\,{{\begin{bmatrix}{7}&{11}\\{8}&{12}\\{9}&{13}\\{10}&{14}\end{bmatrix}}^{\mathrm {T} }}}={\begin{bmatrix}{29}&{32}&{35}&{38}\\{65}&{72}&{79}&{86}\\{101}&{112}&{123}&{134}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6b70aaa9d41bb84acbc0fc7280e94a23a024d0e1)
![{\displaystyle {\frac {\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}{\begin{bmatrix}{2}&{6}\\{3}&{1}\end{bmatrix}}}={\begin{bmatrix}{0.875}&{-0.25}\\{1.25}&{1.5}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6dfcef45050ac17974bc896abde03c1156899133)
![{\displaystyle {{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}^{\begin{bmatrix}{2}&{6}\\{3}&{1}\end{bmatrix}}}={\begin{bmatrix}{-364050.31197887+964690.04071155i}&{-594639.58668283+1155986.4299034i}\\{446972.21255032+511470.08777392i}&{486336.94902566+704877.87824775i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/40553cb70487ac17dff84be20af8f99cba464f28)
![{\displaystyle \log _{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}\left({{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}^{\begin{bmatrix}{2}&{6}\\{3}&{1}\end{bmatrix}}}\right)={\begin{bmatrix}{2.0735030509264+2.2795054463381i}&{4.109459527015+3.5442394256485i}\\{1.8699259345042-1.9535647184507i}&{2.5705958298843-1.6874506503923i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b4c3dbe31df19c8b07ba5c2c213c68732760181d)
![{\displaystyle \log _{7}\left({{7}^{3}}\right)=3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6eed14f0e8ded263ba9a646c0e0878ccb4b79ae6)
![{\displaystyle {\frac {\begin{bmatrix}{24}&{15}\\{17}&{30}\end{bmatrix}}{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}}={\begin{bmatrix}{-4.2692307692308}&{4.0384615384615}\\{2.1923076923077}&{2.1153846153846}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f06418decb20201a6b5967e2dc27e87c89f7bb)
![{\displaystyle \operatorname {round} \left({\frac {\begin{bmatrix}{24}&{15}\\{17}&{30}\end{bmatrix}}{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{-4.269}&{4.038}\\{2.192}&{2.115}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2248caf2f31c9a12675bed0a9fe5367b46e89f79)
= {{1,4},{1,2}}
![{\displaystyle {{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}\,{{\begin{bmatrix}{1}&{5}\\{7}&{9}\end{bmatrix}}^{-1}}}={\begin{bmatrix}{1}&{0}\\{-1.9984014443253\times 10^{-14}}&{0.99999999999999}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a174548bfd5d8c5f1277dbdc7082026c6ffb01c1)
:共轭转置
- 特征值和特征向量
![{\displaystyle eigenvalue\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)=-1.1279462354857}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4153f1dd6a114b6b72a3ef2bdf35c2b81274ed6a)
![{\displaystyle eigenvector\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)={\begin{bmatrix}{-1.6973852602632}\\{0.30597228737293}\\{1}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d25dbe52dd442f74489d76e8ac15b300c49257f9)
![{\displaystyle {{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}\times {eigenvector\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}}={\begin{bmatrix}{1.9145593144827}\\{-0.34512028970549}\\{-1.127946235486}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b5968c358a3da49d1cbd91b8bcda90bf7f82d8dd)
![{\displaystyle {{eigenvector\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}\times {eigenvalue\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}}={\begin{bmatrix}{1.9145593144828}\\{-0.34512028970524}\\{-1.1279462354857}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fffd006e0fa8a187ca30ed4502f89d617f94ad09)
![{\displaystyle \operatorname {round} \left({{{eigenvector\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}\times {eigenvalue\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}}-{{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}\times {eigenvector\left({\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,1\right)}}},\,10\right)={\begin{bmatrix}{0}\\{0}\\{0}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9ce566deb0c6c3bf3302fa70719c7d66b0bb620e)
- 矩陣函數
![{\displaystyle {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}^{-1}={\begin{bmatrix}{-0.33333333333333}&{-1.8333333333333}&{1.5}\\{-0.33333333333333}&{2.1666666666667}&{-1.5}\\{0.66666666666667}&{-0.83333333333333}&{0.5}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/324282bbb53e577e0832cccdeda3738e325eed7c)
![{\displaystyle \operatorname {round} \left({\sqrt {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{0.512+0.828i}&{0.344+0.358i}&{0.764-0.508i}\\{1.108-0.149i}&{2.011-0.065i}&{1.265+0.091i}\\{1.617-0.488i}&{1.98-0.211i}&{2.139+0.299i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/615c9deb067701ecce4fa52a55da3f9bcf7bde9b)
![{\displaystyle \operatorname {round} \left({{\sqrt {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}\times {\sqrt {\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}},\,3\right)={\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/92a020af74cd6e87a006df3253e897cc76f9b9fd)
![{\displaystyle \operatorname {round} \left({\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}},\,3\right)={\begin{bmatrix}{0.44+0.97i}&{0.317+0.009i}&{0.639-0.172i}&{1.36-0.463i}\\{1.097-0.174i}&{2.039-0.002i}&{1.243+0.031i}&{0.183+0.083i}\\{1.635-0.571i}&{2.011-0.005i}&{2.169+0.101i}&{-0.254+0.272i}\\{0.335-0.005i}&{-0.045}&{0.555+0.001i}&{2.949+0.003i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0cd6765ae7b74be8c979f3f81cc9527542880cfb)
![{\displaystyle \operatorname {round} \left({{\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}\times {\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}},\,3\right)={\begin{bmatrix}{1}&{2.061-0.021i}&{3}&{5}\\{5}&{7.008+0.004i}&{6}&{2}\\{7}&{8.989+0.012i}&{8}&{1}\\{2.049-0.008i}&{1.223}&{3.056+0.001i}&{9.008+0.004i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3137b6b9bce0d90da887cb590bf1ff89a48e9f03)
![{\displaystyle {{\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}-{{\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}\times {\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}}}={\begin{bmatrix}{1}&{-0.0609069612035+0.02065600290136i}&{3}&{5}\\{5}&{-0.0081857435936996-0.0037187820564415i}&{6}&{2}\\{7}&{0.011375233491499-0.012178315529462i}&{8}&{1}\\{-0.0491448383185+0.0077259881075695i}&{-0.2233735344013-0.0002865687318072i}&{-0.0556547457662-0.0014408810380774i}&{-0.0081857435939003-0.0037187820564442i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c282a3bb49a159c75132623a02fef0ca25a9446)
![{\displaystyle {{\operatorname {round} \left({{\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}\times {\sqrt {\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}},\,10\right)}-{\begin{bmatrix}{1}&{2}&{3}&{5}\\{5}&{7}&{6}&{2}\\{7}&{9}&{8}&{1}\\{2}&{1}&{3}&{9}\end{bmatrix}}}={\begin{bmatrix}{0}&{0.0609069612-0.0206560029i}&{0}&{0}\\{0}&{0.0081857436000004+0.0037187821i}&{0}&{0}\\{0}&{-0.011375233500001+0.0121783155i}&{0}&{0}\\{0.0491448383-0.0077259881i}&{0.2233735344+0.0002865687i}&{0.0556547458+0.001440881i}&{0.0081857436000004+0.0037187821i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/133bf6f77775213f8695f88425c68cc595f25fa2)
![{\displaystyle \operatorname {round} \left(\log _{2}{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}},\,3\right)={\begin{bmatrix}{0.398+3.532i}&{1.483+1.53i}&{-0.074-2.166i}\\{1.409-0.637i}&{0.52-0.276i}&{2.286+0.39i}\\{1.36-2.081i}&{2.663-0.901i}&{1.667+1.276i}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0abf6ecef501b6a44199ba09775ba5675ce96c51)
![{\displaystyle \operatorname {round} \left({{2}^{\log _{2}{\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}},\,3\right)={\begin{bmatrix}{1}&{2}&{3}\\{5}&{7}&{6}\\{7}&{9}&{8}\end{bmatrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/930a6671e4f920589e35c75051b46ca473d88619)
- 錯誤測試
- 計算失敗:執行函數 "inverse" 發生錯誤 "Module:Complex_Number/Matrix第100行Lua错误:in inverse() :Matrix Error: Singular matrix, can't find its inverse"
- {{0.33823557857999+2.460010873455i,0.81979946670129+1.0142959793242i,0.12214321459583-1.4565156834862i,-0.14436663080365-0.056479668696189i},{0.87893695509153-0.43650773622565i,0.64019128979017-0.17997808325771i,1.327499855358+0.25844615998903i,0.38695747530007+0.010021830631473i},{0.96913088796228-1.4546912509079i,1.7566025594487-0.59978901023376i,1.2334688116638+0.86128912861335i,-0.055701949676983+0.033398421443206i},{0.24389271791696-0.01179203978823i,-0.27314130324697-0.0048620185684112i,0.47740097115575+0.0069817947055361i,2.2189211188093+0.00027073477913376i}}
- {{0.69314718055995,0,0,0},{0,0.69314718055995,0,0},{0,0,0.69314718055995,0},{0,0,0,0.69314718055995}}
- {{0.69314718055995,0},{0,0.69314718055995}}