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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI SELAPARANG: Jurnal Pengabdian Masyarakat Berkemajuan Mandalika Mathematics and Educations Journal Inferensi Journal of Mathematics Education and Science Mathematics and Applications (MAp) Journal Journal of Social Outreach Journal of Research Applications in Community Services Basis : Jurnal Ilmiah Matematika
Hardina Sandariria
Universitas Mulawarman
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Journal : Mathematics and Applications (MAp) Journal

 1 
INVERS MOORE-PENROSE SEBAGAI REPRESENTASI MATRIKS PROYEKSI ORTHOGONAL Sri Wigantono; Moh. Nurul Huda; Qonita Qurrota A'yun; Hardina Sandariria; Dimas Raditya Sahputra; Tuhfatul Janan
MAp (Mathematics and Applications) Journal Vol 5, No 1 (2023)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/map.v5i1.6187

Abstract

The inverse of matrix is one of the important properties of matrix. This properies, especially singular matrix, has been developed by Moore and continued by Penrose. Then, this inverse called Moore-Penrose inverse. The Moore-Penrose invers criteria can represent a projection on a vector space V along W with V and W are orthogonal to each other or can written with W=V^⊥ which is called orthogonal projection matrix on V. This research will present lemmas and theorems related to the Moore-Penrose invers construction of the multiplication matrix. Then, a square matrix is an orthogonal projection matrix on a vector space V if and only if it satisfies two conditions, that are idempotent and symmetric. These two properties are satisfied by matrices I-A^+ A and I-AA^+ which respectively are orthogonal projection matrices on Ker(A) and Ker(A^' ). As a result, the Moore-Penrose inverse A^+ can be constructed from a square matrix A which is an multiplication of several matrices and fulfills certain properties.
ANALISIS DINAMIK MODEL MATEMATIKA PENYEBARAN PENYAKIT KECANDUAN GAME ONLINE DENGAN MEMPERHATIKAN FAKTOR EDUKASI Wigantono, Sri; A'yun, Qonita Qurrota; Sandariria, Hardina; Dani, Andrea Tri Rian; Fauziyah, Meirinda
MAp (Mathematics and Applications) Journal Vol 6, No 2 (2024)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/map.v6i2.10065

Abstract

Kecanduan bermain game online adalah bentuk penggunaan aplikasi permainan yang kurang bijak. Dampak buruk dan banyak masalah sosial muncul akibat dari kecanduan bermain game online.  Pada penelitian ini dibahas model matematika penyebaran penyakit kecanduan bermain game online dengan memperhatikan faktor edukasi. Model ini bertipe SEAR yang terdiri atas empat kompartemen, yaitu Susceptible (rentan), Exposed (terpapar), Addicted (kecanduan), dan Recovered (sembuh). Kemudian, pada penelitian ini ditentukan titik setimbang, bilangan reproduksi dasar, dan dilakukan analisis kestabilan titik setimbang yang sudah diperoleh. Berdasarkan hasil analisis kestabilan titik setimbang, didapat bahwa titik setimbang bebas penyakit model bersifat stabil asimtotis jika bilangan reproduksi dasar bernilai kurang dari satu dan titik setimbang endemik bersifat stabil asimtotis jika bilangan reproduksi dasar bernilai lebih dari satu. Berdasarkan hasil simulasi numerik didapat bahwa ilustrasi kestabilan lokal titik setimbang sesuai dengan hasil analisis yaitu konvergen ke titik setimbangnya. Selain itu, dari hasil numerik juga menunjukkan keefektivitasan faktor edukasi pada model yaitu semakin tinggi tingkat edukasi, maka akan menurunkan populasi yang terpapar dan populasi kecanduan bermain game online.
Co-Authors A'yun, Qonita Qurrota Adawiyah, Rabbiatul Adhitya Ronnie Effendie, Adhitya Ronnie Aminah, Esse Andrea Tri Dani Andrea Tri Rian Dani Asmaidi Asmaidi Asmaidi Auliya Rahman A’yun, Qonita Qurrota Cahyadi, Aldy Fradana Mahaputra Cahyono, Rico Dwi Dala, Maria Alensia Deltin Dani, Andrea Tri Rian Desi Febriani Putri Desi Febriani Putri Devita Dwi Putri Dian Sri Rahmadani Dimas Raditya Dimas Raditya Sahputra Elvita, Melati Fachrian Bimantoro Putra Fahrezi, Korompot Naufal Fauzi, Andri Azmul Fauziyah, Meirinda Fidia Deny Tisna Amijaya Husna Novia indarsih, Indarsih Indriasri Raming Itsar Mangngiri Khairina, Isna Nadia Manggiri, Itsar Meirinda Fauziyah Meirinda Fauziyah Moh. Nurul Huda Moh. Nurul Huda, Moh. Nurul Muhammad Aldani Zen Mulyadi, Taqriri Kamal Munfaati, Rafika Husnia Nazmi Soraya Pridiptama, Raka Putra Putra, Fachrian Bimantoro Putri, Annisa Amalia Putri, Desi Febriani Qonita Qurrota A'yun Qonita Qurrota A'yun Qonita Qurrota A'yun Qonita Qurrota A’yun Rahmadi, Deddy Ramadhanty, Husna Novia Raming, Indriasri Sahputra, Dimas Raditya Said Said, Said Sifriyani, Sifriyani Solikhatun, Solikhatun Sri Wahyuni Sri Wahyuningsih Sri Wigantono Syaripuddin Syaripuddin Syaripuddin Syaripuddin Taqriri Kamal Mulyadi Tuhfatul Janan Tumilaar, Rinancy Uha Isnaini Wahyujati, Mohamad Fahruli Wasono Wasono Wasono Wasono, Wasono Wulandari Wulandari