1) Essence of Linear Algebra
Scalar
Scalar (numbers) fulfill two requirements: Real number that can be used to measure a continuou...
Vectors
Vector Properties
Vector Basics There are three perspectives to consider: Physics perspective Vectors ar...
Basis Vectors
If you do not constrain i hat or j hat, then its possible to reach any point of the coordin...
Vector Multiplication
Formula Input: Scalar (Number) and a vector Output: Vector Stretching out the vector...
Vector Addition
Input: At least 2 vectors Output: One Vector 2D Example vector addition is the only t...
Coordinate Systems
Anyway to translate vectors and sets of numbers is called a coordinate system
Span
Prereq: Linear Combination, Vector Addition, Vector Multiplication Span is the collection of all...
Linear System of Equations
A system of equations consists of unknown variables and list of equations relating them. A Lin...
Matrices
Linear Transformations
Linear Transformation of Matrices Prereq knowledge: Vectors and Basis Vectors, Linear dependent ...
Matrix multiplication and Composition
In order to describe the effects of multiple sequential matrix transformation, such as a rotate a...
Properties
Matrices are rectangular arrays consisting of numbers and are an example of 2nd-order tensors. If...
Non-Linear Transformations
Definition Matrix Exponentiation: Raising a matrix to a power greater than one, as in �2A...
Non-Square Matrices
Matrix Transpose
Basis
basis vectors, linear transformations, matrix multiplications, inverse When changing basis, Orig...
Determinant
Determinant is the scaling factor that if the linear transformation changes any area Scalin...
Dot Product
Dot Product Dot Product can be used to Find out if vector point in the same direction, perpe...
Cross Product
Prereq: Determinant Input: 2 Vectors Output: 1 Vector P is the vector perpendicular to the pa...
Linear Combination
Prereq: Vector addition, Vector multiplication
Eigenvectors and Eigenvalues
Prereq: Change of Basis, Determinants, Linear Transformation, Linear Systems of Equations, span ...