Kutsvaga inverse matrix

Muchinyorwa chino, tichaona kuti inverse matrix chii, uye zvakare, tichishandisa muenzaniso unoshanda, isu tichaongorora kuti ingawanikwa sei tichishandisa yakakosha fomula uye algorithm yezviito zvakatevedzana.

Tsanangudzo ye inverse matrix

Kutanga, ngatirangarirei kuti ndezvipi kudzokorora kuri mumasvomhu. Ngatitii tine nhamba 7. Ipapo inverse yayo ichava 7^-1 or ¹/₇. Kana ukawanza nhamba idzi, mhedzisiro inova imwe, kureva 7 7^-1 = 1.

Zvinenge zvakafanana nematrices. Reverse matrix akadaro anonzi, kuwedzera izvo neicho chepakutanga, tinowana chitupa. Akanyorwa kuti A^-1.

A · A^-1 =E

Algorithm yekutsvaga iyo inverse matrix

Kuti uwane inverse matrix, iwe unofanirwa kukwanisa kuverenga matrices, pamwe nekuva nehunyanzvi hwekuita zvimwe zviito navo.

Izvo zvinofanirwa kucherechedzwa ipapo kuti inverse inogona kuwanikwa chete yeskweya matrix, uye izvi zvinoitwa uchishandisa fomula pazasi:

|A| - matrix determinant;

A^T_M ndiwo matrix akachinjirwa ezvinyorwa zvealgebraic.

Cherechedza: kana iyo determinant iri zero, ipapo inverse matrix haipo.

muenzaniso

Ngatitsvagei matrix A pazasi ndipo pakasiyana nazvo.

mhinduro

1. Kutanga, ngatitsvagei chirevo cheiyo yakapihwa matrix.

2. Zvino ngatigadzirei matrix ine mipimo yakafanana neyekutanga:

Tinofanira kufunga kuti ndedzipi nhamba dzinofanira kutsiva asterisks. Ngatitangei nechepamusoro kuruboshwe chinhu che matrix. Mudiki pairi anowanikwa nekuyambuka mutsara nekoramu mauri, kureva mune ese ari maviri panhamba yekutanga.

Nhamba inosara mushure mekurohwa ndiyo idiki inodiwa, kureva M₁₁ = 8.

Saizvozvo, isu tinowana vadiki kune zvakasara zvinhu zvematrix uye tinowana inotevera mhedzisiro.

3. Isu tinotsanangura matrix ezvinyorwa zvealgebraic. Maitiro ekuzviverengera kune chimwe nechimwe chinhu, isu takafunga mune yakaparadzana.

Somuenzaniso, kune chimwe chinhu a₁₁ algebraic kuwedzera kunoonekwa seizvi:

A₁₁ = (-1)^{1 + 1} M₁₁ = 1 · 8 = 8

4. Ita kushandura kwematrix inoguma yealgebraic akawedzera (kureva, chinjanisa makoramu nemitsara).

5. Inosara chete kushandisa formula iri pamusoro kuti uwane inverse matrix.

Tinogona kusiya mhinduro mune iyi fomu, pasina kupatsanura zvinhu zvematrix nenhamba 11, sezvo mune ino kesi tinowana yakashata mafractional manhamba.

Kutarisa mhinduro

Kuti tive nechokwadi chekuti takawana inverse yematrix yepakutanga, tinogona kuwana chigadzirwa chavo, icho chinofanira kuenzana nematrix ekuzivikanwa.

Nekuda kweizvozvo, takawana iyo identity matrix, zvinoreva kuti takaita zvese nemazvo.