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Me kana Matrikusi na Farko?

Electrical4u
فیلڈ: Karkashin Kuliya da Dukkana
0
China

Matrica na haguji shine matar da ke maimaita grafu kamar yadda ake amfani da ita za a iya garga grafu. Wannan matar zai iya duba [AC] Kamar duk matare, akwai kalamomin da kudin cikin matrica na haguji [AC].
Kudin matar [AC] sun maimaita adadin wurare da kalamomin matar [AC] sun maimaita adadin farkon a cikin grafu. Idan akwai ‘n’ kudin a cikin matar na haguji, yana nufin cewa a cikin grafu akwai ‘n’ wurare. Duk da haka, idan akwai ‘m’ kalamomin a cikin matar na haguji, yana nufin cewa a cikin grafu akwai ‘m’ farko.
incidence matrix

A cikin grafu ko directed graph da aka nuna a tsohon rubutun, akwai 4 wurare da 6 farko. Saboda haka, matrica na haguji don grafu na bi ya shiga zai da 4 kudin da 6 kalamomin.
Akwai kalmomin da suka duba -1, 0, +1 a cikin matar na haguji. Wannan matar ba tabbas ba ce mafi girma da
KCL (Kirchhoff Current Law). Saboda haka, ne a kan KCL zan iya samun cewa,

Na'ura ta farko Yawan
Farko mai fitarwa daga wurar kth  +1
Farko mai baka zuwa wurar kth  -1
Wadanda basu 0

Tsarin Da Zai Yi Matrica Na Haguji

Wadannan suna da tsari na yi matar na haguji :-

  1. Idan wurar kth na da farko mai fitarwa, zan iya rubuta +1.

  2. Idan wurar kth na da farko mai baka, zan iya rubuta -1.

  3. Basa wadanda basu zai iya duba 0.

Misalai Na Matar Na Haguji

incidence matrix

Don grafu da aka nuna a tsohon rubutun, rubuta matar na haguji.
incidence matrix

Matar Na Haguji Da Take Da Tsari

Idan a cikin matar na haguji [AC], an fi kudin da take da tsari, wannan matar na bi ya shiga zai iya duba matar na haguji da take da tsari. Ana bayyana shi da alama [A]. Yawan matar na haguji da take da tsari shine (n-1) × b inda n shine adadin wurare da b shine adadin farko.
Don grafu da aka nuna a tsohon rubutun, matar na haguji da take da tsari zai iya duba :-
reduced incidence matrix
[NOTE :- A cikin matar da aka nuna kudin 4 ana fi]
A nan za a iya gano misali na baya game da matar na haguji da take da tsari. Don grafu da aka nuna a tsohon rubutun, rubuta matar na haguji da take da tsari.
directed graph
Amsa:- Don in yi matar na haguji da take da tsari, kafin so, ya kamata a yi matar na haguji. Matar na haguji shine :-

A nan za a iya yi matar na haguji da take da tsari. Don haka, a kai a fi kudin 2. Matar na haguji da take da tsari shine:-

Wannan shine amsar da aka bukata.
Abubuwan da ya kamata a tabbata

  • Don in tabbatar da adala a matsayin matar na haguji, ya kamata a tabbatar da jamiyar kalamomin.

  • Idan jamiyar kalamomin yana haɗa zuwa 0, yana nufin cewa matar na haguji da aka yi ya fi dace, ba tare da haka.

  • Matar na haguji zai iya amfani da shi a kan directed graph kawai.

  • Adadin kalmomin a cikin kudin waɗanda basu suka duba 0, yana nufin cewa adadin farkon da suka hakki a wurar. Wannan shine kuma degree ta wurar.

  • Rank of complete matar na haguji shine (n-1), inda n shine adadin wurare a cikin grafu.

  • Yawan matar na haguji shine (n × b), inda b shine adadin farko a cikin grafu.

  • Daga matar na haguji da take da tsari, zai iya yi complete matar na haguji tare da kalmomin +1, 0, ko -1, a cikin halin da jamiyar kalamomin yana haɗa zuwa 0.

Source: Electrical4u.

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