Linear Algebra

By the end, you can

• Explain why a vector can be read both as an arrow and as a list of numbers.
• Compute dot products and interpret the sign as a measure of alignment.
• Describe a matrix as a transformation and identify what its columns represent.
• Multiply a matrix by a vector by dotting each row with the vector.
• Explain why matrix multiplication is non-commutative and give an example.
• Compute the determinant of a 2×2 matrix and interpret what a zero determinant means.
• Set up a system of equations as Ax = b and describe how Gaussian elimination solves it.
• Define an eigenvector and eigenvalue using the equation Av = λv.
• Identify PCA, PageRank, and SVD as real-world applications of eigenvectors.