Matrices Elimination
Matrices elimination (or solving system of linear equations) is the very first and fundamental skill throughout Linear Algebra. It's probably the first lesson of all sorts of courses.
Matrices elimination
solving system of linear equations
Rank of Transformation
Means the Dimension of output of a transformation.
Dimension of output of a transformation
Refer to 3Blue1Brown: Inverse matrices, column space and null space
Scalar Projection & Vector Projection
Refer to the note in Pre Linear algebra about understanding Dot product.
Pre Linear algebra
Assume that the vector w projects onto the vector v.Notation:
w
v
Componentᵥw
Eigen-stuffs
Eigenvectors
For a linear transformation, an eigenvector is a vector which, after applying the transformation, stays in the same span.
linear transformation
eigenvector
When we say eigenvectors, we always need to say eigenvectors of a linear transformation.It's the same with…
eigenvectors
eigenvectors of a linear transformation
Matrix multiplication
IT IS A WHOLE NEW AREA ASIDE FROM MATRICES BASIC OPERATIONS.
Vector & basic operations
Definition: vector is a MAGNITUDE with a DIRECTION
Refer to the review pdf.
Lecture video timeline | Links
Matrices intro
Matrices are just a rectangle array of numbers.Prerequisites: Systems of equations
Matrices
Systems of equations
Cross product
Actually the cross product is very very very limited in use, and as fairly often as the dot product.
cross product
dot product
So don’t waste time on this unless having certain use of it.
REMEMBER: A CROSS PRODUCT ONLY HAS USE IN 3-DIMENSIONS, AND ORDER MATTERS, AND GIVES YOU A…
