{"id":1623,"date":"2012-05-16T15:04:41","date_gmt":"2012-05-16T15:04:41","guid":{"rendered":"http:\/\/www.schooltutoring.com\/scholarship\/?p=1623"},"modified":"2014-12-02T08:33:45","modified_gmt":"2014-12-02T08:33:45","slug":"review-of-symmetric-and-skew-symmetric-matrices","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/05\/16\/review-of-symmetric-and-skew-symmetric-matrices\/","title":{"rendered":"Review of Symmetric and Skew-symmetric Matrices"},"content":{"rendered":"

Transpose of a matrix is the matrix obtained by changing its rows into corresponding columns or columns into corresponding rows. The transpose of a m<\/em> \u00d7 n<\/em> matrix is a n<\/em> \u00d7 m<\/em> matrix that results by interchanging the rows and columns of the matrix. The transpose of a matrix is written with the superscript T or \u2018.<\/p>\n

\"\"<\/a><\/p>\n

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 <\/p>\n

Symmetric Matrix<\/strong><\/p>\n

A square matrix is defined as symmetric if it is equal to its transpose, i.e. A = AT<\/sup>. for each element of A, aij<\/sub> = aji<\/sub>.<\/p>\n

Example,<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

As A = AT<\/sup>. A is a symmetric matrix,<\/p>\n

Skew-symmetric Matrix<\/strong><\/p>\n

A square matrix can be a skew-symmetric matrix if its negative is equal to its transpose i.e. \u2013A = AT<\/sup>. For every element of A, , aij<\/sub> = -aji<\/sub>.<\/p>\n

Example,<\/p>\n

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 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

As \u2013A = AT<\/sup>, A is a skew-symmetric matrix.<\/p>\n

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Kingston visit: Tutoring in Kingston.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Transpose of a matrix is the matrix obtained by changing its rows into corresponding columns or columns into corresponding rows. The transpose of a m \u00d7 n matrix is a n \u00d7 m matrix that results by interchanging the rows and columns of the matrix. The transpose of a matrix is written with the superscript […]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[4,14],"tags":[1658,1798,1847],"class_list":["post-1623","post","type-post","status-publish","format-standard","hentry","category-calculus","category-pre-calculus","tag-skewsymmetricmatrix","tag-symmetricmatrix","tag-transponseofmatrix"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=1623"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1623\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=1623"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=1623"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=1623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}