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Advancedlinear-algebramatrix-decompositionseigenvaluesnumerical-methods

Linear Algebra Deep Dive

27 problems·~10h·4 stages

A complete tour of the matrix machinery behind ML, from dot products to spectral decompositions. You will implement row reduction, LU, Cholesky, Gram-Schmidt, power iteration, and PageRank steps from scratch. Suited to learners who want to reason about rank, conditioning, and eigenvalues fluently.

Your progress

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Continue path · Vector Addition

What you will learn

  • Move fluently between vectors, matrices, and linear systems
  • Factorize matrices with LU, Cholesky, QR, and Gram-Schmidt
  • Compute eigenvalues and eigenvectors with power-iteration methods
  • Apply spectral ideas to whitening, PageRank, and low-rank approximation

Before you start

1Vectors and Products

0/7

Rebuild the basics with intent: vector operations, norms, identity matrices, outer products, and the Kronecker product that appears in tensor code.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.

2Matrices and Systems

0/7

Matrix products, transposes, determinants, and rank, plus the eigenpair check and cosine similarity that everything else builds on.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.

3Factorizations

0/6

The matrix decompositions numerical libraries actually run: LU with Doolittle, Cholesky, Gram-Schmidt, QR, power iteration, and rank-1 approximation.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.

4Spectral Applications

0/7

Put the eigen-decomposition to work: normalized eigenvectors, Rayleigh quotients, singular values, whitening, the spectral norm, deflation, and PageRank's stationary distribution.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.

Capstone

Collection

Close the path with one real artifact from the catalog.

The Essence of Linear Algebra

Consolidate the factorizations and spectral ideas with one more pass over the matrix core.