{"id":16660,"date":"2020-01-18T20:18:27","date_gmt":"2020-01-19T01:18:27","guid":{"rendered":"http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/"},"modified":"2020-02-08T09:41:57","modified_gmt":"2020-02-08T14:41:57","slug":"optimization-and-linear-algebra-math-from-the-internet","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16660","title":{"rendered":"Optimization and Linear Algebra\/Math from the Internet"},"content":{"rendered":"

Optimization and Linear Algebra\/Math from the Internet<\/p>\n

First order taylor approximation formula?<\/p>\n

https:\/\/www.thestudentroom.co.uk\/showthread.php?t=1247928<\/a><\/p>\n

Hessian Matrix<\/p>\n

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

"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."<\/p>\n

Use in optimization<\/p>\n

"Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function. That is,<\/p>\n

"<\/p>\n

"Newton’s method in optimization"<\/p>\n

In calculus, Newton’s method is an iterative method for finding the roots of a differentiable function F, which are solutions to the equation F (x) = 0. In optimization, Newton’s method is applied to the derivative f \u2032 of a twice-differentiable function f to find the roots of the derivative (solutions to f \u2032(x) = 0), also known as the stationary points of f. These solutions may be minima, maxima, or saddle points.[1]<\/p>\n

https:\/\/en.wikipedia.org\/wiki\/Newton%27s_method_in_optimization<\/a><\/p>\n

SOLVING LINEAR DIFFERENTIAL EQUATIONS WITH THE LAPLACE TRANSFORM<\/p>\n

https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9781118733639.app6<\/a><\/p>\n

Pointwise supremum of a convex function collection<\/p>\n

is it "I think it is either assumed that the ?? are defined on the same domain ?, or that (following a common convention) we set ??(?)=+\u221e if ?\u2209Dom(??). You can easily check that under this convention, the extended ?? still remain convex and the claim is true."<\/p>\n

https:\/\/math.stackexchange.com\/questions\/402919\/pointwise-supremum-of-a-convex-function-collection?rq=1<\/a><\/p>\n

"The supremum of a set is its least upper bound and the infimum is its greatest<\/p>\n

upper bound."<\/p>\n

https:\/\/www.math.ucdavis.edu\/~hunter\/m125b\/ch2.pdf<\/a><\/p>\n

Sine and Cosine Values<\/p>\n

https:\/\/math.stackexchange.com\/questions\/1553990\/easy-way-of-memorizing-values-of-sine-cosine-and-tangent\/1554126<\/a><\/p>\n

Barrier Function<\/p>\n

"<\/p>\n

Barrier function. In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value on a point increases to infinity as the point approaches the boundary of the feasible region of an optimization problem.<\/p>\n

"<\/p>\n

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

Trace: Marix<\/p>\n

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

Determinant<\/p>\n

"The determinant of a matrix A is denoted det(A), det A, or |A|. Geometrically, it can be viewed as the volume scaling factor of the linear transformation described by the matrix. This is also the signed volume of the n-dimensional parallelepiped spanned by the column or row vectors of the matrix. The determinant is positive or negative according to whether the linear mapping preserves or reverses the orientation of n-space."<\/p>\n

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

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

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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 in optimization "Hessian matrices are … <\/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-16660","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":16660,"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":16660,"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":16689,"url":"http:\/\/bangla.sitestree.com\/?p=16689","url_meta":{"origin":16660,"position":2},"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":16682,"url":"http:\/\/bangla.sitestree.com\/?p=16682","url_meta":{"origin":16660,"position":3},"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":[]},{"id":16691,"url":"http:\/\/bangla.sitestree.com\/?p=16691","url_meta":{"origin":16660,"position":4},"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":16698,"url":"http:\/\/bangla.sitestree.com\/?p=16698","url_meta":{"origin":16660,"position":5},"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":[]}],"_links":{"self":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16660","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=16660"}],"version-history":[{"count":1,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16660\/revisions"}],"predecessor-version":[{"id":16709,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16660\/revisions\/16709"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16660"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}