Linear Algebra Notes

Revisiting Linear Algebra

Vectors

The traditional explanation for vectors is basically 'anything with magnitude and direction.' While this is true in many contexts, vectors can be understood from various perspectives depending on their application.

• Physics: Vectors are often represented as arrows pointing in space, defined by their magnitude and direction.

• Computer Science: Vectors are usually understood as ordered lists of numbers, essential for representing and manipulating data in algorithms and data structures. They help computer scientists and data scientists conceptualize and analyze complex datasets, facilitating tasks such as pattern recognition, machine learning, and data visualization.

• Mathematics: Vectors can be abstracted from these perspectives and are primarily concerned with operations such as addition and scalar multiplication.

Vectors also play a crucial role in manipulating space and conceptualizing numbers:

• Space Manipulation: Vectors describe positions, movements, and forces in a coordinate system. This application is vital in physics for representing physical quantities like velocity, and in computer graphics for representing positions, directions, and transformations in three-dimensional space.

• Conceptualizing Numbers: Vectors serve as a powerful mathematical tool, enabling complex operations and transformations through coordinates and algebraic rules.

Vector Example: