Linear Systems #
How systems of linear equations are represented and solved using matrices.
- the study of vectors and rules to manipulate vectors
- describe multiple linear equations solved simultaneously
- connect algebraic equations with matrix representations
Idea of Closure #
performing a specific operation (like addition or multiplication) on members of a set always produces a result that belongs to the same set
idea of closure is fundamental to defining a Vector space because it ensures that performing arithmetic operations (addition and scalar multiplication) on vectors within a set does not produce a new element outside that set.
Machine Learning View #
Many machine learning models can be abstracted as:
\[ y = Wx + b \]x → input data
W → weight, how model transforms it
𝑏 → bias adjusts the result
y → is the output
Models transform input vectors using matrices.