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
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Subspace
https://www.wolframalpha.com/input/?i=subspace
"What is an affine set?
A set is called “affine” iff for any two points in the set, the line through them is contained in the set. In other words, for any two points in the set, their affine combinations are in the set itself. Theorem 1. A set is affine iff any affine combination of points in the set is in the set itself."
https://www.cse.iitk.ac.in/users/rmittal/prev_course/s14/notes/lec3.pdf [good one to check]
linear/conic/affine/convex combination
https://observablehq.com/@eliaskal/point-combinations-linear-conic-affine-convex
Related Course:
https://www.cse.iitk.ac.in/users/rmittal/prev_course/s14/course_s14.html
"In linear algebra, the column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of a matrix is the image or range of the corresponding matrix transformation.
en.wikipedia.org › wiki › Row_and_column_spaces
Row and column spaces - Wikipedia
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Row and column spaces
https://en.wikipedia.org/wiki/Row_and_column_spaces
"Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:"
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Infimum and supremum
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A set T of real numbers (hollow and filled circles), a subset S of T (filled circles), and the infimum of S. Note that for finite, totally ordered sets the infimum and the minimum are equal.
A set A of real numbers (blue circles), a set of upper bounds of A (red diamond and circles), and the smallest such upper bound, that is, the supremum of A (red diamond).
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set T is the greatest element in T that is less than or equal to all elements of S, if such an element exists.[1] Consequently, the term greatest lower bound (abbreviated as GLB) is also commonly used.[1]
The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set T is the least element in T that is greater than or equal to all elements of S, if such an element exists.[1] Consequently, the supremum is also referred to as the least upper bound (or LUB).[1]
