{"id":16682,"date":"2020-01-26T00:20:45","date_gmt":"2020-01-26T05:20:45","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/?p=16682"},"modified":"2020-01-30T21:39:36","modified_gmt":"2020-01-31T02:39:36","slug":"misc-math-might-relate-to-optimization","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16682","title":{"rendered":"Misc. Math. Might Relate to Optimization"},"content":{"rendered":"

find the equation for a line<\/p>\n

http:\/\/www.webmath.com\/_answer.php<\/a><\/p>\n

Parametric forms for lines and vectors<\/h1>\n

https:\/\/www.futurelearn.com\/courses\/maths-linear-quadratic-relations\/0\/steps\/12128<\/a><\/p>\n

Solving Systems of Linear Equations Using Matrices<\/h1>\n

https:\/\/www.mathsisfun.com\/algebra\/systems-linear-equations-matrices.html<\/a><\/p>\n

Affine Space
\n”
\n\"\"<\/a><\/p>\n

”<\/p>\n

Subspace
\nhttps:\/\/www.wolframalpha.com\/input\/?i=subspace<\/a><\/p>\n

“What is an affine set?
\nA set<\/strong> is called \u201caffine<\/strong>\u201d iff for any two points in the set<\/strong>, the line through them is contained in the set<\/strong>. In other words, for any two points in the set<\/strong>, their affine<\/strong> combinations are in the set<\/strong> itself. Theorem 1. A set<\/strong> is affine<\/strong> iff any affine<\/strong> combination of points in the set<\/strong> is in the set<\/strong> itself.”
\nhttps:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/notes\/lec3.pdf<\/a> [good one to check]<\/p>\n

linear\/conic\/affine\/convex combination<\/p>\n

https:\/\/observablehq.com\/@eliaskal\/point-combinations-linear-conic-affine-convex<\/a><\/p>\n

Related Course:
\nhttps:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/course_s14.html<\/a><\/p>\n

“<\/strong><\/em>In linear algebra, the column space (also called the range<\/strong> or image) of a matrix<\/strong> A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix<\/strong> is the image or range<\/strong> of the corresponding matrix<\/strong> transformation.
\nen.wikipedia.org \u203a wiki \u203a Row_and_column_spaces<\/a><\/p>\n

Row and column spaces – Wikipedia<\/a><\/h3>\n

“<\/strong><\/em><\/p>\n

Row and column spaces<\/h1>\n

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

“Any linear combination of the column vectors of a matrix A<\/em> can be written as the product of A<\/em> with a column vector:”<\/p>\n

”<\/p>\n

Infimum and supremum<\/h1>\n

From Wikipedia, the free encyclopedia<\/p>\n

Jump to navigation<\/a>Jump to search<\/a>\"\"<\/a>
\nA set T<\/em> of real numbers (hollow and filled circles), a subset S<\/em> of T<\/em> (filled circles), and the infimum of S<\/em>. Note that for finite, totally ordered sets the infimum and the minimum<\/a> are equal.<\/p>\n

\"\"<\/a>
\nA set A<\/em> of real numbers (blue circles), a set of upper bounds of A<\/em> (red diamond and circles), and the smallest such upper bound, that is, the supremum of A<\/em> (red diamond).<\/p>\n

In mathematics<\/a>, the infimum<\/strong> (abbreviated inf<\/strong>; plural infima<\/strong>) of a subset<\/a> S<\/em> of a partially ordered set<\/a> T<\/em> is the greatest element<\/a> in T<\/em> that is less than or equal to all elements of S<\/em>, if such an element exists.[1]<\/a> Consequently, the term greatest lower bound<\/em> (abbreviated as GLB<\/em>) is also commonly used.[1]<\/a><\/p>\n

The supremum<\/strong> (abbreviated sup<\/strong>; plural suprema<\/strong>) of a subset S<\/em> of a partially ordered set T<\/em> is the least element<\/a> in T<\/em> that is greater than or equal to all elements of S<\/em>, if such an element exists.[1]<\/a> Consequently, the supremum is also referred to as the least upper bound<\/em> (or LUB<\/em>).[1]<\/a><\/p>\n

”
\nhttps:\/\/en.wikipedia.org\/wiki\/Infimum_and_supremum<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

find the equation for a line http:\/\/www.webmath.com\/_answer.php Parametric forms for lines and vectors https:\/\/www.futurelearn.com\/courses\/maths-linear-quadratic-relations\/0\/steps\/12128 Solving Systems of Linear Equations Using Matrices https:\/\/www.mathsisfun.com\/algebra\/systems-linear-equations-matrices.html Affine Space ” ” Subspace https:\/\/www.wolframalpha.com\/input\/?i=subspace “What is an affine set? A set is called \u201caffine\u201d iff for any two points in the set, the line through them is contained in the set. … <\/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":[1908,182],"tags":[],"class_list":["post-16682","post","type-post","status-publish","format-standard","hentry","category-math-and-statistics-for-data-science-and-engineering","category---blog","item-wrap"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":63958,"url":"http:\/\/bangla.sitestree.com\/?p=63958","url_meta":{"origin":16682,"position":0},"title":"Misc: Optimization: Machine Learning: Data Science Resources","author":"Sayed","date":"June 3, 2021","format":false,"excerpt":"http:\/\/web.mit.edu\/15.053\/www\/AMP-Chapter-09.pdf https:\/\/www.cs.cmu.edu\/~anupamg\/adv-approx\/lecture14.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization\/ https:\/\/www.futurelearn.com\/info\/courses\/maths-linear-quadratic-relations\/0\/steps\/12128 https:\/\/www.mathsisfun.com\/algebra\/systems-linear-equations-matrices.html https:\/\/www.wolframalpha.com\/input\/?i=subspace https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/notes\/lec3.pdf https:\/\/observablehq.com\/@eliaskal\/point-combinations-linear-conic-affine-convex https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/course_s14.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-might-relate-to-optimization\/ http:\/\/bangla.salearningschool.com\/recent-posts\/part-x-engineering-optimization-mathematical-optimization\/ https:\/\/www.dr-eriksen.no\/teaching\/GRA6035\/2010\/lecture4.pdf https:\/\/www.mathsisfun.com\/calculus\/concave-up-down-convex.html https:\/\/www-ljk.imag.fr\/membres\/Anatoli.Iouditski\/cours\/convex\/chapitre_3.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/www.thestudentroom.co.uk\/showthread.php?t=1247928 https:\/\/en.wikipedia.org\/wiki\/Hessian_matrix https:\/\/en.wikipedia.org\/wiki\/Newton%27s_method_in_optimization https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9781118733639.app6 http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/en.wikipedia.org\/wiki\/Interior-point_method https:\/\/web.stanford.edu\/~boyd\/papers\/rt_cvx_sig_proc.html Must Read https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/ivantash-optimization_methods_and_their_applications_in_dsp.pdf https:\/\/www.researchgate.net\/publication\/269211254_The_analysis_and_optimization_algorithms_of_the_electronic_circuits_design good one http:\/\/www.bcamath.org\/documentos_public\/courses\/Nogales_2012-13_02_18-22.pdf https:\/\/en.wikipedia.org\/wiki\/Convex_analysis https:\/\/www.khanacademy.org\/search?page_search_query=Optimization%20problems%20(calculus) http:\/\/bangla.salearningschool.com\/recent-posts\/overview-on-optimization-concepts-from-the-internet\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization-machine-learning\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-data-science-machine-learning-optimization-vector-pca-basis-covariance\/ https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse-row-operations-gauss-jordan.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-for-data-science-engineering-and-or-optimization\/","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16691,"url":"http:\/\/bangla.sitestree.com\/?p=16691","url_meta":{"origin":16682,"position":1},"title":"Optimization, Data Science, Math","author":"Sayed","date":"January 28, 2020","format":false,"excerpt":"Optimization Problem: Advances in Missile Guidance, Control, and Estimation Preview: https:\/\/play.google.com\/books\/reader?id=A2PMBQAAQBAJ&hl=en_GB&pg=GBS.PR14 https:\/\/books.google.ca\/books?id=A2PMBQAAQBAJ&pg=PA595&lpg=PA595&dq=force+moment+interaction+with+thrusters&source=bl&ots=BruxnXwLzp&sig=ACfU3U39G-l3xDzbotOBJHcMV5uR7DkciQ&hl=en&sa=X&ved=2ahUKEwjZpsT44afnAhXRJt8KHfPYCroQ6AEwCnoECAoQAQ#v=onepage&q=force%20moment%20interaction%20with%20thrusters&f=false \"What is the difference between affine and linear? 4 Answers. A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so\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":16629,"url":"http:\/\/bangla.sitestree.com\/?p=16629","url_meta":{"origin":16682,"position":2},"title":"Misc. Basic Concepts From Linear Algebra","author":"Sayed","date":"January 12, 2020","format":false,"excerpt":"\"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.\u2026","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image.png?resize=525%2C300 1.5x, https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image.png?resize=700%2C400 2x"},"classes":[]},{"id":16689,"url":"http:\/\/bangla.sitestree.com\/?p=16689","url_meta":{"origin":16682,"position":3},"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":71308,"url":"http:\/\/bangla.sitestree.com\/?p=71308","url_meta":{"origin":16682,"position":4},"title":"What is a subspace?","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 a subspace?","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":71310,"url":"http:\/\/bangla.sitestree.com\/?p=71310","url_meta":{"origin":16682,"position":5},"title":"What are the related ideas of subspace?","author":"Sayed","date":"October 3, 2021","format":false,"excerpt":"If you can, answer the question below: Write your answer in the comment box. What are the related ideas of subspace?","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\/16682","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=16682"}],"version-history":[{"count":2,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16682\/revisions"}],"predecessor-version":[{"id":16728,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16682\/revisions\/16728"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16682"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}