Linear algebra

Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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Matrix transformations

Understanding how we can map one set of vectors to another set. Matrices used to define linear transformations.
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All content in “Matrix transformations”

Transformations and matrix multiplication

You probably remember how to multiply matrices from high school, but didn't know why or what it represented. This tutorial will address this. You'll see that multiplying two matrices can be view as the composition of linear transformations.

Inverse functions and transformations

You can use a transformation/function to map from one set to another, but can you invert it? In other words, is there a function/transformation that given the output of the original mapping, can output the original input (this is much clearer with diagrams). This tutorial addresses this question in a linear algebra context. Since matrices can represent linear transformations, we're going to spend a lot of time thinking about matrices that represent the inverse transformation.

Finding inverses and determinants

We've talked a lot about inverse transformations abstractly in the last tutorial. Now, we're ready to actually compute inverses. We start from "documenting" the row operations to get a matrix into reduced row echelon form and use this to come up with the formula for the inverse of a 2x2 matrix. After this we define a determinant for 2x2, 3x3 and nxn matrices.