Essential Mathematical Concepts for Machine Learning-Linear Algebra

Essential Mathematical Concepts for Machine Learning-Linear Algebra

We will start with Linear Algebra basics. I might be posting 2 or 3 more articles on Linear Algebra to cover those topics which are relevant to machine learning. The topics to be discussed are listed as follows:-

In this particular article, we will start with Linear Algebra basics. I might be posting 2 or 3 more articles on Linear Algebra to cover those topics which are relevant to machine learning. The topics to be discussed are listed as follows:-

  1. Vectors
  2. Vector Spaces and Subspaces
  3. Linear Span
  4. Column Space
  5. Null Space

*Vectors:- *It is an object that has both magnitudes as well as the direction. Geometrically, we can visualize a vector as a directed line segment whose length gives the magnitude of the vector and arrow gives the direction.

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In machine learning, we use vectors to represent features and labels of the input data like age, salary, etc. Here in this example, V is a two- dimensional vector from the field of Real Numbers.

*Vector Space:- *A vector space is a set V of vectors on which the vector addition and vector multiplication are defined such that,

  1. (V,+) is an abelian group.
  2. The dot product between real numbers and vector v is defined in such a way that for all “a” belongs to Real numbers and v belongs to the vector space V such that a.v should belong to the vector space V.
  3. For all ‘a’ belongs to real numbers (R) and v,w belongs to V(vector space), a(v+w)=a.v+a.w
  4. For all a,b belongs to R and v belongs to V, (a+b).v = a.v+b.v
  5. For all a,b belongs to R and v belongs to V, (ab).v=a.(b.v)
  6. (Unitary law) 1 belongs to R and v belongs to V, 1.v belongs to V.

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