An introduction to an informative and factual blog post about linear algebra You can learn interactively at your own pace and in the comfort of your own home. It’s hard to imagine how much easier it can possibly be. Linear algebra is a geometric approach that has been used by mathematicians since the 1800s. Linear Algebra is a branch of mathematics and analytical geometry whose main focus is on geometric objects (like points, lines, planes, and spaces) and the relationships among these objects (like dot products). The linear algebra topics explained here include vector spaces, linear transformations, matrix multiplication & determinant, orthogonal matrices & quadratic forms. The purpose of this website is to provide a comprehensive reference on linear algebra. By reading this article you will understand why the following is true: A few definitions: According to how it is presented, linear algebra can seem like a very abstract and lifeless topic. It is not until you understand some basic concepts (like vector spaces and their dimensions) and some basic operations (like addition and multiplication of vectors), that it becomes clear how useful linear algebra really is in the study of our universe. Just like any other science, mathematics has its own terms that must be learned in order to become familiar with the language used by mathematicians. The rest of this article will explain some basic linear algebra concepts in an easy to understand manner. A Vector Space is a set of elements called Vectors, which are used to represent points in space. Given any two points in space, there is a line segment connecting them, the length of which depends on their distance apart. The set of all points represented by vectors in this manner is Vector Space, which can be represented geometrically by lines connecting these points to each other. An example of a vector space that cooks will find familiar is the set of ingredients that make up recipes. For example, if you have flour and sugar, those are separate vectors. If you combine these two ingredients by adding an egg and baking it at a certain temperature for a period of time, a new vector is created - a cookie vector. Some recipes call for sugar and cinnamon to be added to the cookie recipe instead of just flour and sugar. These new vectors have not been encountered yet in the set of ingredients; they are new vectors that can be discovered through experimentation or research into other recipes. The rule that defines the operations that can be performed on these vectors (i.e., combining them with other vectors) is known as the associative property. The way in which it is defined is by saying that the addition of two vectors is the same as the addition of their corresponding elements added together, the multiplication of two vectors is the same as multiplying one vector by another, and so on. The associative property can be demonstrated graphically by drawing a circle around all the elements in a vector space. It can also be demonstrated geometrically by drawing connecting lines between all the points that are represented by different vectors. This concept often brings about confusion because it can seem at first that being able to rearrange or combine two vectors in an arbitrary manner makes linear algebra an open ended topic, which it certainly is not.
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