INVERS MOORE-PENROSE SEBAGAI REPRESENTASI MATRIKS PROYEKSI ORTHOGONAL

Sri Wigantono, Moh. Nurul Huda, Qonita Qurrota A'yun, Hardina Sandariria, Dimas Raditya Sahputra, Tuhfatul Janan

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.

Keywords


projection matrix, orthogonal projection matrix, Moore-Penrose inverse

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DOI: https://doi.org/10.15548/map.v5i1.6187

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