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Misc. Math for Data Science, Engineering, and/or Optimization

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 complex numbers—except for the zero vector, which is assigned zero.[1]

A pseudonorm (seminorm), on the other hand, is allowed to assign zero to some non-zero vectors (in addition to the zero vector).[2]

The term "norm" is commonly used to refer to the vector norm in Euclidean space. It is known as the "Euclidean norm" (see below) which is technically called the L2-norm. 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 vector space on which a norm is defined is called a normed vector space. 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."

https://en.wikipedia.org/wiki/Norm_(mathematics)

What is Linear programming?

"Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. "

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

Linear programs are problems that can be expressed in canonical form as

{\displaystyle {\begin{aligned}&{\text{Maximize}}&&\mathbf {c} ^{\mathrm {T} }\mathbf {x} \\&{\text{subject to}}&&A\mathbf {x} \leq \mathbf {b} \\&{\text{and}}&&\mathbf {x} \geq \mathbf {0} \end{aligned}}}"

https://en.wikipedia.org/wiki/Linear_programming

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Sayed Ahmed

BSc. Eng. in Comp. Sc. & Eng. (BUET)
MSc. in Comp. Sc. (U of Manitoba, Canada)
MSc. in Data Science and Analytics (Ryerson University, Canada)
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