Karan Parekhkaranparekh.hashnode.net·Jan 22, 2023Linear TransformationCore concept Transformation is another word for function. A function takes in some input, transforms it, and spits out an output. This function or transformation is represented by a matrix. To better understand it, consider the following matrix. $$A ...1 like·57 readsLinear Algebramatrices
Karan Parekhkaranparekh.hashnode.net·Jan 14, 2023Gaussian ReductionTwo simultaneous equations Consider the following system of two simultaneous equations $$\begin{array}{r} & 3a + b = 8 \quad...(1) \\ & a - 2b = 5 \quad...(2) \\ \end{array} $$ We can solve it by multiplying equation (1) by 2 and adding it to equatio...90 readsLinear Algebramatrices
Karan Parekhkaranparekh.hashnode.net·Jan 27, 2023Matrix DeterminantsA simple but important prerequisite for this topic is to understand how linear transformations transform the vector space around it. If you don't then you can read my article on Linear Transformation and come back here for Determinants. Core concept ...63 readsLinear Algebradeterminants
Karan Parekhkaranparekh.hashnode.net·Feb 1, 2023Eigenvectors and EigenvaluesPrerequisites Linear Transformation and Determinants are the two concepts one needs to be clear about before attempting to learn what Eigenvectors and Eigenvalues are. Once familiar with them, the core concept is pretty simple to grasp. Core concept ...54 readsLinear AlgebraMatrix
Karan Parekhkaranparekh.hashnode.net·Jan 27, 2023Matrix DeterminantsA simple but important prerequisite for this topic is to understand how linear transformations transform the vector space around it. If you don't then you can read my article on Linear Transformation and come back here for Determinants. Core concept ...63 readsLinear Algebradeterminants
Karan Parekhkaranparekh.hashnode.net·Jan 22, 2023Linear TransformationCore concept Transformation is another word for function. A function takes in some input, transforms it, and spits out an output. This function or transformation is represented by a matrix. To better understand it, consider the following matrix. $$A ...1 like·57 readsLinear Algebramatrices
Karan Parekhkaranparekh.hashnode.net·Jan 19, 2023Matrix InversionPre-requisite To develop an intuition for Matrix Inversion it is important to be familiar with the concepts of Linear Transformation and Matrix Determinants. Please read these articles if you need a refresher. Core The Inverse of a matrix depends on ...63 readsLinear AlgebraMatrix
Karan Parekhkaranparekh.hashnode.net·Jan 14, 2023Gaussian ReductionTwo simultaneous equations Consider the following system of two simultaneous equations $$\begin{array}{r} & 3a + b = 8 \quad...(1) \\ & a - 2b = 5 \quad...(2) \\ \end{array} $$ We can solve it by multiplying equation (1) by 2 and adding it to equatio...90 readsLinear Algebramatrices
