{"id":3423,"date":"2015-04-12T01:23:13","date_gmt":"2015-04-12T06:23:13","guid":{"rendered":"http:\/\/www.ssc.wisc.edu\/~jfrees\/?page_id=3423"},"modified":"2015-08-16T09:54:31","modified_gmt":"2015-08-16T14:54:31","slug":"basic-operations","status":"publish","type":"page","link":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-9-technical-supplement-elements-of-matrix-algebra\/basic-operations\/","title":{"rendered":"Basic Operations"},"content":{"rendered":"<h1>Scalar Multiplication<\/h1>\n<p>Let \\(\\mathbf{A}\\) by a \\(n\\times k\\) matrix and let \\(c\\) be a real number. That is, a real number is a \\(1\\times 1\\) matrix and is also called a <em>scalar<\/em>. Multiplying a scalar \\(c\\) by a matrix \\(\\mathbf{A}\\) is denoted by \\(c\\mathbf{A}\\) and defined by \\begin{equation*} c\\mathbf{A}=\\left( \\begin{array}{cccc} ca_{11} &#038; ca_{12} &#038; \\cdots &#038; ca_{1k} \\\\ \\vdots &#038; \\vdots &#038; \\ddots &#038; \\vdots \\\\ ca_{n1} &#038; ca_{n2} &#038; \\cdots &#038; ca_{nk} \\end{array} \\right) . \\end{equation*} For example, suppose that \\(c=10\\) and \\begin{equation*} \\mathbf{A}=\\left( \\begin{array}{cc} 1 &#038; 2 \\\\ 6 &#038; 8 \\end{array} \\right) \\text{   then   }\\mathbf{B}=c\\mathbf{A}=\\left( \\begin{array}{cc} 10 &#038; 20 \\\\ 60 &#038; 80 \\end{array} \\right) . \\end{equation*} Note that \\(c\\mathbf{A}=\\mathbf{A}c\\). <\/p>\n<p><div class=\"alignleft\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-9-technical-supplement-elements-of-matrix-algebra\/some-special-matrices\/\" title=\"Some Special Matrices\">&#9668 Previous page<\/a><\/div><div class=\"alignright\"><a href=\"https:\/\/users.ssc.wisc.edu\/~ewfrees\/regression\/basic-linear-regression\/2-9-technical-supplement-elements-of-matrix-algebra\/basic-operations\/addition-and-subtraction-of-matrices\/\" title=\"Addition and Subtraction of Matrices\">Next page &#9658<\/a><\/div><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Scalar Multiplication Let \\(\\mathbf{A}\\) by a \\(n\\times k\\) matrix and let \\(c\\) be a real number. That is, a real number is a \\(1\\times 1\\) matrix and is also called a scalar. Multiplying a scalar &hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3415,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"jetpack_post_was_ever_published":false},"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P8cLPd-Td","acf":[],"_links":{"self":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3423"}],"collection":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/comments?post=3423"}],"version-history":[{"count":2,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3423\/revisions"}],"predecessor-version":[{"id":4805,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3423\/revisions\/4805"}],"up":[{"embeddable":true,"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/pages\/3415"}],"wp:attachment":[{"href":"https:\/\/users.ssc.wisc.edu\/~ewfrees\/wp-json\/wp\/v2\/media?parent=3423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}