{"id":16689,"date":"2020-01-28T20:48:10","date_gmt":"2020-01-29T01:48:10","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-for-data-science-engineering-and-or-optimization\/"},"modified":"2020-02-08T09:40:31","modified_gmt":"2020-02-08T14:40:31","slug":"misc-math-for-data-science-engineering-and-or-optimization","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16689","title":{"rendered":"Misc. Math for Data Science, Engineering, and\/or Optimization"},"content":{"rendered":"

What is the Inverse of a Matrix?<\/h2>\n

https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse.html<\/a><\/p>\n

What is Norm?
\n“In linear algebra<\/a>, functional analysis<\/a>, and related areas of mathematics<\/a>, a norm<\/strong> is a function<\/a> that satisfies certain properties pertaining to scalability and additivity, and assigns a strictly positive real number<\/a> to each vector<\/a> in a vector space<\/a> over the field of real or complex numbers<\/a>\u2014except for the zero vector<\/a>, which is assigned zero.[1]<\/a><\/p>\n

A pseudonorm (seminorm)<\/strong>, on the other hand, is allowed to assign zero to some non-zero vectors (in addition to the zero vector).[2]<\/a><\/p>\n

The term “norm” is commonly used to refer to the vector norm in Euclidean space<\/a>. It is known as the “Euclidean norm” (see below<\/a>) which is technically called the L2-norm<\/a>. The Euclidean norm maps a vector to its length in Euclidean space. Because of this, the Euclidean norm is often known as the magnitude<\/a>.”<\/p>\n

“A vector space on which a norm is defined is called a normed vector space<\/a>. Similarly, a vector space with a seminorm is called a semi normed vector space. It is often possible to supply a norm for a given vector space in more than one way.”<\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Norm_(mathematics)<\/a><\/p>\n

What is Linear programming?<\/h1>\n

“Linear programming<\/strong> (LP<\/strong>, also called linear optimization<\/strong>) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model<\/a> whose requirements are represented by linear relationships<\/a>. ”<\/p>\n

“More formally, linear programming is a technique for the optimization<\/a> of a linear<\/a> objective function<\/a>, subject to linear equality<\/a> and linear inequality<\/a> constraints<\/a>. Its feasible region<\/a> is a convex polytope<\/a>, which is a set defined as the intersection<\/a> of finitely many half spaces<\/a>, each of which is defined by a linear inequality. Its objective function is a real<\/a>-valued affine (linear) function<\/a> defined on this polyhedron. A linear programming algorithm<\/a> finds a point in the polytope<\/a> where this function has the smallest (or largest) value if such a point exists.<\/p>\n

Linear programs are problems that can be expressed in canonical form<\/a> as<\/p>\n

\"{\\displaystyle”<\/p>\n

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

*** . *** . ***
\nNote: Older short-notes from this site are posted on Medium: <\/strong><\/em>https:\/\/medium.com\/@SayedAhmedCanada<\/a><\/p>\n

*** . *** *** . *** . *** . ***<\/p>\n

Sayed Ahmed<\/strong>
\n<\/em>
\nBSc. Eng. in Comp. Sc. & Eng. (BUET)<\/strong><\/em>
\nMSc. in Comp. Sc. (U of Manitoba, Canada)<\/strong><\/em>
\nMSc. in Data Science and Analytics (Ryerson University, Canada)<\/strong><\/em>
\nLinkedin<\/strong>: https:\/\/ca.linkedin.com\/in\/sayedjustetc<\/a>
\n<\/em><\/p>\n

Blog<\/strong>: http:\/\/Bangla.SaLearningSchool.com<\/a>, http:\/\/SitesTree.com<\/a><\/em>
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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 the field of real or … <\/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":[1910,1908,182],"tags":[],"class_list":["post-16689","post","type-post","status-publish","format-standard","hentry","category-ai-ml-ds-rl-dl-nn-nlp-data-mining-optimization","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":16701,"url":"http:\/\/bangla.sitestree.com\/?p=16701","url_meta":{"origin":16689,"position":0},"title":"Misc. Math. Data Science. Machine Learning. Optimization. Vector, PCA, Basis, Covariance","author":"Sayed","date":"January 30, 2020","format":false,"excerpt":"Misc. Math. Data Science. Machine Learning. Optimization. Vector, PCA, Basis, Covariance Orthonormality: Orthonormal Vectors \"In linear algebra, two vectors in an inner product space are orthonormal if they are orthogonal and unit vectors. A set of vectors form an orthonormal set if all vectors in the set are mutually orthogonal\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":"https:\/\/i0.wp.com\/bangla.sitestree.com\/wp-content\/uploads\/2020\/01\/image-8-e1580436936625.png?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":63958,"url":"http:\/\/bangla.sitestree.com\/?p=63958","url_meta":{"origin":16689,"position":1},"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":16641,"url":"http:\/\/bangla.sitestree.com\/?p=16641","url_meta":{"origin":16689,"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":16660,"url":"http:\/\/bangla.sitestree.com\/?p=16660","url_meta":{"origin":16689,"position":3},"title":"Optimization and Linear Algebra\/Math from the Internet","author":"Sayed","date":"January 18, 2020","format":false,"excerpt":"Optimization and Linear Algebra\/Math from the Internet First order taylor approximation formula? https:\/\/www.thestudentroom.co.uk\/showthread.php?t=1247928 Hessian Matrix https:\/\/en.wikipedia.org\/wiki\/Hessian_matrix \"In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables.\" Use\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":16698,"url":"http:\/\/bangla.sitestree.com\/?p=16698","url_meta":{"origin":16689,"position":4},"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":16682,"url":"http:\/\/bangla.sitestree.com\/?p=16682","url_meta":{"origin":16689,"position":5},"title":"Misc. Math. Might Relate to Optimization","author":"Sayed","date":"January 26, 2020","format":false,"excerpt":"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\u2026","rel":"","context":"In "Math and Statistics for Data Science, and Engineering"","block_context":{"text":"Math and Statistics for Data Science, and Engineering","link":"http:\/\/bangla.sitestree.com\/?cat=1908"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image-6.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image-6.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/bangla.salearningschool.com\/wp-content\/uploads\/2020\/01\/image-6.png?resize=525%2C300 1.5x"},"classes":[]}],"_links":{"self":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16689","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=16689"}],"version-history":[{"count":2,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16689\/revisions"}],"predecessor-version":[{"id":16727,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16689\/revisions\/16727"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16689"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}