Week 7 — Linear algebra I

Mathematical foundations I: linear algebra & numerical methods · Implement

Easy

Phase 2 — Mathematical foundations I: linear algebra & numerical methods

Overview

Vector spaces, span, basis, dimension

Mode this week: implement. Match the work to that mode (operating model): implement ships running code; read/diagram ships a doc; deploy/benchmark ships a measured run. Personal dates, checkboxes, and the RPG layer stay in a learner journal.

Core deliverable

Problem set + concept map

Optional depth

Prove one important claim, implement one component from scratch, and verify it numerically.

Week loop (from the cookiecutter journal)

• Mon — Theory: Vector spaces, span, basis, dimension
• Tue — Build: start the core deliverable above
• Wed — Systems / papers: one paper or system note (see below if this week has assigned reading)
• Thu — Eval / interview: write the four evidence items
• Fri — Algorithmic Forge: From-scratch matrix or recurrence solver (45-90 min; Core)

Forge theme: Matrix multiplication, Gaussian elimination, matrix exponentiation, recurrences

Leetcode Darbar (parallel)

This week's band (7-30): Math, bit manipulation, divide and conquer, recursion, backtracking. Production connection: Linear algebra, probability, statistics, optimization.

Standard: one aligned problem. Auror: the five-slot queue on the Darbar page. Tracker stays in the learner journal.

Topics: backtracking · bit manipulation · divide and conquer · math · recursion

• Binary Tree Paths · easy · backtracking
• Count Number Of Maximum Bitwise Or Subsets · medium · bit manipulation
• Convert Sorted Array To Binary Search Tree · easy · divide and conquer
• Divisor Game · easy · math
• Reverse String · easy · recursion

Evidence contract

Every core week records all four (cookiecutter journal/weeks/week_007.md):

1. Code / implementation (or the design artifact on a writing week)
2. Benchmark / result
3. Design doc / technical explanation
4. Retrospective / learning note (Sailboat: destination, wind, anchor, rocks, heading)

On this site

• Dot product & norm
• Matrix multiplication
• Eigenvalues
• SVD
• PCA

Official Tensor-to-Tenant

• Curriculum browser
• Milestone gates
• Weekly operating model
• Leetcode Darbar
• 36-week on-ramp
• Source repo

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