Te Tāpiri me te Tango i waenganui i ngā Matrices
Pendahuluan
Ko te matihiko he kohinga tau kua whakaritea ki ngā rarangi me ngā pou. Ka whakamahia ngā matihiko i roto i ngā momo marautanga, tae atu ki te pāngarau, te ahupūngao, te ōhanga, me te pūtaiao rorohiko. Ko ētahi o ngā mahi taketake ka taea te mahi me ngā matihiko ko te tāpiri me te tango. He mahi taketake ēnei e whakamahia pinepine ana hei whakaoti rapanga uaua i roto i ngā momo marautanga pūtaiao.
Ka matapakihia e tēnei tuhinga te whakamāramatanga, ngā ture, me ngā tauira o te whakamahinga o te tāpiri me te tango i waenga i ngā matihiko me tō rātou whakamahinga i te ao tūturu.
Te Mārama ki te Matrix
He tapawhā rite te hanganga o ngā huānga he m ngā rarangi me te n ngā pou. Ko ngā huānga o te matrix he tau te nuinga, ā, ka taea te tautuhi i ia huānga mā ngā tohu e rua: te rarangi me te pou.
Ko tētahi tauira o tētahi matihiko A 2×2 e whai ake nei:
\[ A = \begin{bmatrix}
he_{11} me he_{12} \\
he_{21} me he_{22} \\
\end{bmatrix} \]
Kei hea:
– Ko \(a_{11}\) te huānga i te rarangi tuatahi, te pou tuatahi.
– Ko \(a_{12}\) te huānga i te rarangi tuatahi, te pou tuarua.
– Ko \(a_{21}\) te huānga i te rarangi tuarua, te pou tuatahi.
– Ko \(a_{22}\) te huānga i te rarangi tuarua, te pou tuarua.
Te Mahi Tāpiri i waenga i ngā matrix
Ko te tāpiri matihiko he mahi e mahia ana i runga i ngā matihiko e rua mā te tāpiri i ō rāua huānga e rite ana. Kia taea ai te tāpiri i ngā matihiko e rua, me rite te rahi.
Ngā Ture Tāpiri
Mena he mxn ngā matihiko A me B, ko te tapeke o ngā matihiko A me B ko te matihiko C, he mxn anō hoki. Ka tatauhia ia huānga o te matihiko C mā te tāpiri i ngā huānga e rite ana o ngā matihiko A me B:
\[ C = A + B \]
Mā te tuhipoka, ka taea te tuhi i ngā huānga o te matihiko C:
\[ c_{ij} = a_{ij} + b_{ij} \]
Tauira Tāpiri
Me kī kei a tātou ngā matihiko e rua, A me B, penei:
\[ A = \begin{bmatrix}
1 me te 2
3 me te 4
\end{bmatrix}, \quad B = \begin{bmatrix}
5 me te 6
7 me te 8
\end{bmatrix} \]
Mā te tāpiri i ngā matihiko A me B ka puta te matihiko C:
\[ C = A + B = \begin{bmatrix}
1 + 5 me te 2 + 6
3 + 7 me te 4 + 8
\end{bmatrix} = \begin{bmatrix}
6 me te 8
10 me te 12
\end{bmatrix} \]
Te Mahi Tangohanga Intermatrix
Ko te tango i waenga i ngā matihiko he mahi e mahia ana mā te tango i ngā huānga e rite ana o ngā matihiko e rua. Pērā i te tāpiri, me rite te rahi o ngā matihiko e rua hei tango.
Ture Whakaiti
Mena he rua ngā matihiko o A me B, ko te hua o te tango i ngā matihiko A me B ko te matihiko D, he rahi m x n anō hoki. Ka tatauhia ia huānga o te matihiko D mā te tango i ngā huānga e rite ana mai i ngā matihiko A me B:
\[ D = A – B \]
Mā te tuhipoka, ka taea te tuhi i ngā huānga o te matihiko D:
\[ d_{ij} = a_{ij} – b_{ij} \]
Tauira o te Tangohanga
Me kī kei a tātou ngā matihiko e rua, A me B, penei:
\[ A = \begin{bmatrix}
10 me te 20
30 me te 40
\end{bmatrix}, \quad B = \begin{bmatrix}
1 me te 2
3 me te 4
\end{bmatrix} \]
Mā te tango i waenga i ngā matihiko A me B ka puta te matihiko D:
\[ D = A – B = \begin{bmatrix}
10 – 1 me te 20 – 2
30 – 3 me te 40 – 4
\end{bmatrix} = \begin{bmatrix}
9 me te 18
27 me te 36
\end{bmatrix} \]
Ngā tono tāpiri me te tango i te matihiko
1. Ōhanga me te Pūtea: I roto i ngā tauira ōhanga, ka whakamahia ngā matihiko hei tohu i ngā raraunga pūtea pēnei i ngā whakapaunga me ngā moni whiwhi. Ka taea te whakamahi i te whakarāpopototanga matihiko hei tatau i te tapeke o ngā whakapaunga, o ngā moni whiwhi rānei o ngā tari, o ngā peka rānei.
2. Ahupūngao me te Hangarau: I roto i te ahupūngao me te hangarau, ka whakamahia ngā matihiko hei tohu i ngā pūnaha whārite rārangi e whakauru ana i ngā taurangi maha i te wā kotahi. Me whakamahi te tāpiri me te tango matihiko hei whakahaere me te whakangawari i ēnei whārite.
3. Whakairoiro Rorohiko: I roto i ngā whakairoiro rorohiko, ka whakamahia ngā matihiko hei 'whakarerekē' i ngā mea i roto i te wāhi 3D pērā i te hurihanga, te whakawhiti, me te tauine. Ka āwhina ngā mahi tāpiri me te tango i ēnei momo mahi.
4. Te Tukatuka Whakaahua: He huarahi paerewa ngā matihiko hei whakaatu i ngā whakaahua matihiko. Ka taea te whakamahi i ngā mahi tāpiri me te tango matihiko mō ngā mahi tukatuka whakaahua pēnei i te whakaranu, te tātari, me te kimi taha.
Whakamutunga
He mea nui te tāpiri me te tango i waenga i ngā matihiko ki te matawai rārangi, ā, he whānuitia te whakamahinga i roto i ngā momo marautanga. Mā ngā ture māmā e whakahaere ana i ēnei mahi ka taea e tātou te mahi i ngā mahi uaua maha, ā, ka whai wāhi nui hoki ki te whakaoti rapanga mahi maha.
Mā te mārama ki ngā ariā taketake me te whakamahinga o aua ariā ka waiho hei tūāpapa pakari mō te ako me te whakamahi anō ki ngā raruraru o te ao tūturu. Ko te whāinga o tēnei tuhinga he whakarato i te māramatanga ki ngā kaipānui mō ngā mātāpono taketake o te tāpiri me te tango i waenga i ngā matihiko, hei tūāpapa mō te ako anō i te taurangi rārangi me ōna whakamahinga i roto i ngā momo mara.
