CodeForCrack - Linear Algebra

Understand the definition and properties of vector spaces, and learn to identify subspaces and compute spans.

Understand the definition and properties of vector spaces, and learn to identify subspaces and compute spans.

Learn to determine if vectors are linearly dependent or independent using fundamental methods.

Study matrix types, properties, operations, and special matrices like orthogonal and projection matrices.

Represent quadratic expressions in matrix form and classify them based on definiteness.

Represent and solve linear systems using matrix notation, Gaussian elimination, and consistency checks.

Find eigenvalues and eigenvectors, solve characteristic equations, and explore their properties.

Understand determinant calculation, matrix rank, nullity, and the Rank-Nullity Theorem.

Explore orthogonal and vector projections onto subspaces with real-world applications.

Break down matrices into lower and upper triangular matrices and use them to solve linear systems.

Understand SVD, compute singular values and vectors, and explore applications like dimensionality reduction.

Linear Algebra