Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
Group automorphisms in abstract algebra
Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem
From playlist Abstract algebra
Finding Eigenvalues and Eigenvectors
In studying linear algebra, we will inevitably stumble upon the concept of eigenvalues and eigenvectors. These sound very exotic, but they are very important not just in math, but also physics. Let's learn what they are, and how to find them! Script by Howard Whittle Watch the whole Math
From playlist Mathematics (All Of It)
An identity matrix under matrix multiplication serves a similar role to the number 1, when it comes to integer multiplication, i.e. any number times 1, remains that number. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until Udemy
From playlist Introducing linear algebra
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
For more details on the Mathemalchemy project, see mathemalchemy.org
From playlist 3D printing
The inverse of a matrix is a similarly sized matrix such that the multiplication of the two matrices results in the identity matrix. In this video we look at an example of this. You can learn more about Mathematica on my Udemy course at https://www.udemy.com/mathematica/ PS! Wait until
From playlist Introducing linear algebra