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When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skew\u2010symmetric orthogonal solutions are respectively given. As an auxiliary, an algorithm is provided to compute the least squares symmetric orthogonal solutions, and meanwhile an example is presented to show that it is reasonable.<\/jats:p>","DOI":"10.1155\/2012\/471573","type":"journal-article","created":{"date-parts":[[2012,12,24]],"date-time":"2012-12-24T21:00:54Z","timestamp":1356382854000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Constrained Solutions of a System of Matrix Equations"],"prefix":"10.1155","volume":"2012","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0494-4928","authenticated-orcid":false,"given":"Qing-Wen","family":"Wang","sequence":"first","affiliation":[]},{"given":"Juan","family":"Yu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,12,24]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"269","article-title":"The inverse problem of symmetric orthogonal matrices and its optimal approximation","volume":"28","author":"Meng C. 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