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#linear-algebra

Introduction In the realm of linear algebra, the concepts of linear dependency and linear non-dependency hold significant importance. These terms help us analyze the relationships between vectors and…

Norm A norm of a vector is a scalar value that defines the magnitude or length of the vector in a vector space. The norm of a vector is useful for various mathematical operations, such as determining …

Plane P is defined by A(2,0,0), B(0,4,0), C(0,0,2) Question: Check if point D(-3,2,4) is in the plane P Answer: Lets Assume A to be origin in local coordinate system Vector BA = B - A (column wise subtraction) = <-2, 4, 0> Vector CA = C - A…

Vector Space A group is a mathematical structure consisting of a set of elements and a binary operation that takes two elements and returns a third element in the set. The operation must satisfy four …

In Mathematics, a vector is a quantity that has both magnitude and direction. It is typically represented as an arrow in a space of any number of dimensions and can be represented algebraically as an …

Let \(M\) be an \(n \times n\) matrix. A scalar \(\lambda \) is an eigenvalue of \(M\) if there is a non-zero vector \(x\) (called eigenvector) s.t.: $$M x = \lambda x$$ Eigenvalues and eigenvectors a…

This article is mostly about how to use the Python module, NumPy, for matrix calculation and is written as a reference for the one who takes or will take EECS 16A at Berkeley. What is NumPy? NumPy i…

Deep learning plays a key role in modern AI (Artificial Intelligence) and machine learning. It uses a series of ‘neurons’ structured in layers to break down the data and extract the outputs we need. T…

Mathematics of vectors Imagine if you are given two row vectors a=[a1,a2,a3,.....an] b=[b1,b2,b3,.....bn] Mathematically lets learn some basic operations on vectors 1.Addition what would a+b res…

Vector Space: We define vector space as a set of all elements that are closed under vector addition and scalar multiplication operations. (closed means that after some operation on vector you will aga…