Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
GENERALIZED AND CONDITIONAL INVERSES MAT 457 7 2 + 0 2 5
Ön Koşul Dersleri Students are assumed to be familiar with Linear Algebra I-II.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. HALİM ÖZDEMİR Dersi Verenler Dersin Yardımcıları Res.Assist. Emre Kişi and Res.Assist. Tuğba Petik Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı In many of applied sciences, particularly, in the theory of linear models it is involved the solutions of a system of linear equations and functions of the solutions. A unified theory to treat all situations that involves the use of the generalized and conditional inverse of matrices are discussed in this course. Dersin İçeriği Introduction, Preliminaries, Definition and basic theorems of generalized inverse, Systems of linear equations, Generalized inverses for special matrices, Computing formulas for the g-inverse, Applications, Conditional inverse, Hermit form of matrices, Applications.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she demonstrates the culture of general mathematics 1 - 2 - 3 - 4 - 14 - 15 - A - B - 2 - He/she identifies the concept of a generalized inverse of any matrix. 1 - 2 - 3 - 4 - 14 - 15 - A - B - 3 - He/she evaluates generalized inverses of special types of matrices by practical ways. 1 - 2 - 3 - 4 - 14 - 15 - A - B - 4 - He/she describes the conditional inverse of any matrix. 1 - 2 - 3 - 4 - 14 - 15 - A - B - 5 - He/she describes Hermit form of any matrix. 1 - 2 - 3 - 4 - 14 - 15 - A - B - 6 - He/she practices these matters. 1 - 2 - 3 - 4 - 14 - 15 - A - B -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 14:Self Study 15:Problem Solving Ölçme Yöntemleri: A:Testing B:Oral Exam

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction [2] page 38, [1] pages 95-96
2 Preliminaries [1] pages 96-103
3 Definition and basic theorems of generalized inverse [1] pages 96-103
4 Systems of linear equations [1] pages 103-104
5 Generalized inverses for special matrices [1] pages 105-107
6 Generalized inverses for special matrices (continue) [1] pages 105-107
7 Computing formulas for the g-inverse [1] pages 107-118
8 Computing formulas for the g-inverse (continue) [1] pages 107-118
9 Applications [1] pages 129-135
10 Midterm exam
11 Conditional inverse [1] pages 119-125
12 Conditional inverse (continue) [1] pages 119-125
13 Hermitic form of matrices [1] pages 125-129
14 Applications [1] pages 129-137

#### Kaynaklar

Ders Notu [1] Freanklin A. GRAYBILL, Introduction to matrices with applications in statistics, Wadsworth publishing company, Inc., Belmont California, 1969.
Ders Kaynakları [2] C. Radhakrishna RAO, Sujit Kumar MITRA, Generalized inverse of matrices and its applications, John Wiley & Sons Inc., Canada, 1971.
[3] Thomas N. F. GREVILLE, Adi BEN-ISRAEL, Generalized Inverses Theory and Applications, John Wiley & Sons, Inc., Canada, 1974.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking.

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 55
KisaSinav 1 15
KisaSinav 2 15
KisaSinav 3 15
Toplam 100
Yıliçinin Başarıya Oranı 60
Finalin Başarıya Oranı 40
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 12 12
Quiz 3 9 27
Final examination 1 12 12
Toplam İş Yükü 115
Toplam İş Yükü /25(s) 4.6
Dersin AKTS Kredisi 4.6
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