Linear Algebra

Basis & Dimension

Advanced judgment in basis selection and dimensionality calibration. For teens who already use linear algebra and need to avoid subtle, costly mistakes.

Goal:

Learn how basis vectors define dimensionality.

3Lessons

6Micro-lessons

AdvancedDifficulty

Lesson 1

Ambiguity in Basis Selection

Judging basis vectors when the system is unstable or unclear.

Start2 Micro-lessons

Micro lesson 1

Hidden Instability in Basis Choice

Micro lesson 2

Overfitting the Basis to the Situation

Lesson 2

Dimension Collapse & Expansion

Recognizing when dimensionality changes unexpectedly and its consequences.

Start2 Micro-lessons

Micro lesson 1

Dimension Loss Under Constraint

Micro lesson 2

False Expansion of Dimension

Lesson 3

Long-Term Effects of Basis Misjudgment

How repeated basis errors compound and distort systems over time.

Start2 Micro-lessons

Micro lesson 1

Compounding Basis Errors

Micro lesson 2

When to Recalibrate the Basis