Current Language EN
English English Türkçe Türkçe Español Español Português Português Pусский Pусский Filipino Filipino Tiếng Việt Tiếng Việt हिन्दी हिन्दी العربية العربية বাংলা বাংলা Deutsch Deutsch 中文 中文
Research Article

Spectral Theorem: Diagonalizable Symmetric Matrix

582 reads
Noriebelle Balbontin
Psych Educ Multidisc J, 2022, 4 (7), 727-728, DOI: https://doi.org/10.5281/zenodo.7140908, ISSN 2822-4353
Verified on SciChain · token #641 of SciMatic Articles (ERC-1155, 1,000,000 tokens)
Contract 0x0E596B4b…F05eF8 · mint transaction · verify the record
Proof of record · recorded 2026-10-17 · anchored on SciChain · Verify (opens in a new tab) · record

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.

Keywords linear algebra canonical forms Spectral Theorem Symmetric Matrix Diagonalizable
Author 1
View Publication Certificate View PDF Cite This Article Back to Archives

The team behind this paper

1 author, 1 institution.

This paper Iloilo State College of Fisheries — Philippines Iloilo State College of… 1 author Noriebelle Balbontin — corresponding author NB Noriebelle Balbontin ✉

Readership

344 reads over 34 months.

February 2024 November 2026

On SciChain

This article is token #641 of SciMatic Articles (ERC-1155): 1,000,000 tokens, minted once, never more. The chain also stores a fingerprint (SHA-256) of the article's record, so anyone can check that it has not been altered.

HolderWalletTokens
SciMatic 0xc35709…277732 100,000 (10%)
Noriebelle Balbontin 0xa6a63B…Fa3a3F 900,000 (90%)
Content hash 0xa40e534527eb54fa6192da755bd0c8fc7b750ed9234c54637b7bb90bd77d23bb
View on the explorer Verify the record Mint transaction

Bibliographic Information

Noriebelle Balbontin (2022). Spectral Theorem: Diagonalizable Symmetric Matrix, Psychology and Education: A Multidisciplinary Journal, 4(7): 727-728
Bibtex Citation
@article{noriebelle_balbontin2022pemj,
author = {Noriebelle Balbontin},
title = {Spectral Theorem: Diagonalizable Symmetric Matrix},
journal = {Psychology and Education: A Multidisciplinary Journal},
year = {2022},
volume = {4},
number = {7},
pages = {727-728},
doi = {10.5281/zenodo.7140908},
url = {https://scimatic.org/show_manuscript/641}
}
APA Citation
Balbontin, N., (2022). Spectral Theorem: Diagonalizable Symmetric Matrix. Psychology and Education: A Multidisciplinary Journal, 4(7), 727-728. https://doi.org/10.5281/zenodo.7140908

Author Information

  • To change your profile photo, login to scimatic.org, go to your profile and change the photo.
  • Any photo that shows your face will do: we crop it to your head and shoulders and give it a plain background automatically.
  • To sign in, go to Sign in and enter the e-mail address registered with the article: we e-mail you a one-time sign-in link (there is no password).
  • In case of any other problem, contact your editor directly or write to us at info @ scimatic.org