Spectral Theorem: Diagonalizable Symmetric Matrix

Noriebelle  Balbontin,

Spectral Theorem: Diagonalizable Symmetric Matrix

Discipline: Education

Abstract:

In linear algebra, is the canonical forms of a linear transformation. Given a particularly nice basis for the vector spaces in which one is working, the matrix of a linear transformation may also be particularly nice, revealing some information about how the transformation operates on the vector space.The spectral theorem provides a sufficient criterion for the existence of a particular canonical form. Specifically, the spectral theorem states that if A equals the transpose of A, then A is diagonalizable:there exists an invertible matrix B such that B-1 AB is a diagonal matrix.

References:

Amanonce, J. T., and Maramag, A. M. (2020). Licensure examination performance and academic achievement of teacher education graduates. International Journal of Evaluation and Research in Education, 9( 3):510-516. DOI: 10.11591/ijere.v9i3.20614
Antiojo L. P.. (2017). Performance of education graduates in the licensure examination for teachers (LET). PEOPLE: International Journal of Social Sciences, 3(2):1363-1384. DOI:10.20319/pijss.2017.32.13631384
Archana, S., and Kumbakonam, U. R. (2016). Role of a teacher in English language teaching (ELT). International Journal of Educational Science and Research.7:1-4.
Canale M. (1983). From communicative competence to communicative language pedagogy. Language and Communication.2-14.
Canale, M., and Swain, M. (1980). Theoretical bases of communicative approaches to second language teaching and testing. Applied Linguistics, 1 (1):1-47. http://www.uefap.com/tefsp/bibliog/canale_swain.pdf
Chan-Rabanal, G., and Manzano, M. T. S. (2018). Licensure Examination for Teachers (LET) Performance of the University of Northern Philippines Graduates. International Journal of Scientific & Engineering Research, 9(12): 510-522.
CHED. (2004). Commission on Higher Education Order (CMO) No. 30, series 2004. The revised teacher education curriculum.
Dumitriu, C., Timofti, I. C., and Dumitriu, G. (2014) Communicative Skill and/or Communication Competence? Procedia - Social and Behavioral Sciences, 141. DOI:10.1016/j.sbspro.2014.05.085
Foster-Cohen, S. H. (2001). Communicative Competence: Linguistic Aspects. International Encyclopedia of the Social & Behavioral Sciences.
Francisco, C. D. C., and Celon, L. C. (2020). Teachers' instructional practices and its effects on students' academic performance. International Journal of Scientific Research in Research Paper, 6(7):64-71.
Hattie, J. A. C. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. New York, NY: Routledge. https://doi.org/10.4324/9780203887332 \
Kalaw, M. T. B. (2017). Trend of De La Salle Lipa Education Graduates' Performance in the Licensure Examination for Teachers. International Journal of Evaluation and Research in Education, 6(2): 138-149.
Kiessling, C., and Fabry, G. (2021). What is communicative competence and how can it be acquired? GMS Journal of Medical Education, 38(3): Doc49.. doi: 10.3205/zma001445
Liu, X. (2010). Arousing the College Students' Motivation in Speaking English through Role- Play. International Education Studies, 3(1): 136-144
Martirosyan, N. M., Hwang, E., and Wanjohi, R. (2015). Impact of English Proficiency on Academic Performance of International Students. Journal of International Students Peer, 5(1):60-71.
Moe, M. M. (2019). Teaching grammar through communicative language teaching. International Journal of Advance Research and Development, 4(8);75-77. www.ijarnd.com
Nordquist, R. (2019). Communicative competence definition, examples, and glossary. https://www.thoughtco.com/what-is-communicative-competence-1689768
Pagaduan-Apostol, E. S..(2017). Assertiveness, self-esteem and academic performance in speech and oral communication of Filipino junior secondary teacher education students. Asia Pacific Journal of Multidisciplinary Research, 5(3): 36-42.
Poolsawad, K., Kanjanawasee, S., and Wudthayagorn, J. (2015). Development of an English Communicative Competence Diagnostic Approach. Procedia - Social and Behavioral Sciences, 191:759–763. doi: 10.1016/j.sbspro.2015.04.462
Rezida A. Fahrutdinova, Rifat R. Fahrutdinov. Et Al. (2016). The model of forming communicative competence of students in the process of teaching the English Language. International Journal of Environmental & Science Education.;11(6):1285-1294.
Sanderson, C., and Paliwal, K. K. (1999). Multi-modal person verification system based on face profiles and speech. ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications, 947-950. DOI: 10.1109/ISSPA.1999.815828
Souriyavongsa, T. (2013). Factors causes students low English language learning: a case study in the National University of Laos. International Journal of English Language Education .;1(1):179-192.
Stefanson, T. O. (2012). Factors Affecting English Language Learners' Literacy in US Schools.. http://www2.uwstout.edu/content/lib/thesis/2012/2012stefansont.pdf
Tuan, V. V. (2017). Communicative Competence of the Fourth Year Students: Basis for Proposed English Language Program. English Language Teaching, 10(7):104-122. http://doi.org/10.5539/elt.v10n7p104
Vorwerg, C. (2015). Communicative competence: Linguistic. Aspects International Encyclopedia of the Social & Behavioural Sciences (Second Edition).
Yu, X. (2021). A Study on the Role of Sentence Structure Analysis in English Learning. Open Access Library Journal.;8(9). DOI: 10.4236/oalib.1107859
Yufrizal, H. (2017). Teachers and students' perceptions of communicative competence in English as a foreign language in Indonesia. Educational Research and Reviews, 12(17):867- 883. DOI: 10.5897/ERR2017.3243