{"id":11471,"date":"2021-07-05T23:16:11","date_gmt":"2021-07-05T23:16:11","guid":{"rendered":"https:\/\/papersspot.com\/blog\/2021\/07\/05\/help-understanding-linear-independence-of-solutions-on-odes\/"},"modified":"2021-07-05T23:16:11","modified_gmt":"2021-07-05T23:16:11","slug":"help-understanding-linear-independence-of-solutions-on-odes","status":"publish","type":"post","link":"https:\/\/papersspot.com\/blog\/2021\/07\/05\/help-understanding-linear-independence-of-solutions-on-odes\/","title":{"rendered":"help understanding linear independence of solutions on ODE&#8217;s"},"content":{"rendered":"<p>I don&#8217;t understand how to proof that if X and Y in R^n are linearly independent as vectors with every component being a scalar function of &#8216;t&#8217;, therefore as functions of &#8216;t&#8217;, then the vector X(t=u) is linearly independent of Y(t=u) in R^n with &#8216;u&#8217; being a particular value of the Real variable &#8216;t&#8217; and viceversa. I don&#8217;t seem to understand how the later implies the first. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>I don&#8217;t understand how to proof that if X and Y in R^n are linearly independent as vectors with every component being a scalar function of &#8216;t&#8217;, therefore as functions of &#8216;t&#8217;, then the vector X(t=u) is linearly independent of Y(t=u) in R^n with &#8216;u&#8217; being a particular value of the Real variable &#8216;t&#8217; and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10],"class_list":["post-11471","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-writing"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/11471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=11471"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/11471\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=11471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=11471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=11471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}