{"id":16629,"date":"2020-01-12T22:18:35","date_gmt":"2020-01-13T03:18:35","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/?p=16629"},"modified":"2020-01-12T22:18:35","modified_gmt":"2020-01-13T03:18:35","slug":"misc-basic-concepts-from-linear-algebra","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16629","title":{"rendered":"Misc. Basic Concepts From Linear Algebra"},"content":{"rendered":"

"<\/strong>Vector Space<\/p>\n

Description<\/h2>\n

A vector space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. Wikipedia<\/a>"<\/strong><\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Vector_space<\/a><\/p>\n

What is F in the Vector Space<\/strong>
\n\"\"<\/a><\/p>\n

"The general definition of a vector space<\/strong> allows scalars to be elements of any fixed field F<\/strong>. The notion is then known as an F<\/strong>–vector spaces<\/strong> or a vector space<\/strong> over F<\/strong>. A field is, essentially, a set of numbers possessing addition, subtraction, multiplication and division operations."
\nhttps:\/\/en.wikipedia.org\/wiki\/Vector_space<\/a><\/p>\n

"<\/p>\n

"What is a span of a set of vectors?<\/p>\n

The span of a set of vectors<\/strong> is the set<\/strong> of all linear combinations of the vectors<\/strong>. For example, if and then the span<\/strong> of v1 and v2 is the set<\/strong> of all vectors<\/strong> of the form sv1+tv2 for some scalars s and t. The span of a set of vectors<\/strong> in gives a subspace of .<\/p>\n

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

Linear Algebra basics<\/a><\/h3>\n


\nhttps:\/\/www.rpi.edu \u203a ~mitchj \u203a handouts \u203a linalg
\n<\/a>"<\/p>\n

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

Gaussian elimination – Wikipedia<\/a><\/h3>\n


\nhttps:\/\/en.wikipedia.org \u203a wiki \u203a Gaussian_elimination
\n<\/a><\/p>\n

Gaussian elimination<\/strong>, also known as row reduction, is an algorithm in linear algebra for solving a system of linear equations. It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients.<\/p>\n

"
\nhttps:\/\/en.wikipedia.org\/wiki\/Gaussian_elimination<\/a><\/p>\n

Linear Maps<\/strong>
\n"In mathematics, a linear map<\/strong> (also called a linear mapping<\/strong>, linear transformation<\/strong> or, in some contexts, linear<\/strong> function) is a mapping<\/strong> V \u2192 W between two modules (for example, two vector spaces) that preserves (in the sense defined below) the operations of addition and scalar multiplication.
\n<\/a><\/p>\n

Linear map – Wikipedia<\/a><\/h3>\n


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

https:\/\/en.wikipedia.org \u203a wiki \u203a Linear_map
\n<\/a>"<\/p>\n

*** . *** . *** . *** . *** . *** . *** . ***<\/p>\n","protected":false},"excerpt":{"rendered":"

"Vector Space Description A vector space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. Wikipedia" https:\/\/en.wikipedia.org\/wiki\/Vector_space What is F … <\/p>\n

Continue reading<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[182],"tags":[],"class_list":["post-16629","post","type-post","status-publish","format-standard","hentry","category---blog","item-wrap"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":16689,"url":"http:\/\/bangla.sitestree.com\/?p=16689","url_meta":{"origin":16629,"position":0},"title":"Misc. Math for Data Science, Engineering, and\/or Optimization","author":"Sayed","date":"January 28, 2020","format":false,"excerpt":"What is the Inverse of a Matrix? https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse.html What is Norm? \"In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that satisfies certain properties pertaining to scalability and additivity, and assigns a strictly positive real number to each vector in a vector space over\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":71342,"url":"http:\/\/bangla.sitestree.com\/?p=71342","url_meta":{"origin":16629,"position":1},"title":"What is the notation to represent a vector of real numbers or real-complex numbers?","author":"Sayed","date":"October 3, 2021","format":false,"excerpt":"If you can, answer the question below: Write your answer in the comment box. What is the notation to represent a vector of real numbers or real-complex numbers?","rel":"","context":"In "Matrix and Signal Processing"","block_context":{"text":"Matrix and Signal Processing","link":"http:\/\/bangla.sitestree.com\/?cat=1944"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16641,"url":"http:\/\/bangla.sitestree.com\/?p=16641","url_meta":{"origin":16629,"position":2},"title":"Misc. Optimization. Machine Learning","author":"Sayed","date":"January 14, 2020","format":false,"excerpt":"\"What is machine learning optimization? Optimization is the most essential ingredient in the recipe of machine learning algorithms. It starts with defining some kind of loss function\/cost function and ends with minimizing the it using one or the other optimization routine.Sep 5, 2018\" https:\/\/towardsdatascience.com\/demystifying-optimizations-for-machine-learning-c6c6405d3eea Ordered vector space \"Given a vector\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"A-B","src":"https:\/\/i0.wp.com\/mathworld.wolfram.com\/images\/equations\/VectorOrdering\/Inline1.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":16698,"url":"http:\/\/bangla.sitestree.com\/?p=16698","url_meta":{"origin":16629,"position":3},"title":"Misc Math, Data Science, Machine Learning, PCA, FA","author":"Sayed","date":"January 29, 2020","format":false,"excerpt":"\"In mathematics, a set B of elements (vectors) in a vector space V is called a basis, if every element of V may be written in a unique way as a (finite) linear combination of elements of B. The coefficients of this linear combination are referred to as components or\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"A=(a_(ij))","src":"https:\/\/i0.wp.com\/mathworld.wolfram.com\/images\/equations\/HermitianMatrix\/Inline1.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":71366,"url":"http:\/\/bangla.sitestree.com\/?p=71366","url_meta":{"origin":16629,"position":4},"title":"Show linear vector space using matrix-vector multiplication. y = AC = [a1 a2 a3…an] * [c1 c2 c3 …. cn]. [c1 c2 c3 …. cn] is in column form","author":"Sayed","date":"October 3, 2021","format":false,"excerpt":"If you can, answer the question below: Write your answer in the comment box. Show linear vector space using matrix-vector multiplication. y = AC = [a1 a2 a3...an] * [c1 c2 c3 .... cn]. [c1 c2 c3 .... cn] is in column form","rel":"","context":"In "Matrix and Signal Processing"","block_context":{"text":"Matrix and Signal Processing","link":"http:\/\/bangla.sitestree.com\/?cat=1944"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":70892,"url":"http:\/\/bangla.sitestree.com\/?p=70892","url_meta":{"origin":16629,"position":5},"title":"What is a Vector Space?","author":"Sayed","date":"September 18, 2021","format":false,"excerpt":"If you can, answer the question below: Write your answer in the comment box. What is a Vector Space?","rel":"","context":"In "Matrix and Signal Processing"","block_context":{"text":"Matrix and Signal Processing","link":"http:\/\/bangla.sitestree.com\/?cat=1944"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16629","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16629"}],"version-history":[{"count":1,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16629\/revisions"}],"predecessor-version":[{"id":16631,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16629\/revisions\/16631"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16629"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16629"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16629"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}