Linear Algebra

Vectors, Matrices, Eigenvalues, and SVD.

Not started3 min explanation

Visualize, practice, and deep-dive material are optional—use only what helps you learn.

Explanation

A focused 3-minute explanation using the topic's authored material.

Learning goals and prerequisites

After this lesson

Reason geometrically about matrix operations
Use decompositions to solve and compress models
Estimate numerical and computational consequences of a design

Helpful before starting

Algebra and coordinate geometry
Functions and basic derivatives
Comfort with indexed notation

Start here

Linear Algebra, in plain language

Vectors, Matrices, Eigenvalues, and SVD. Vectors, matrices, projections, decompositions, and tensor operations are the computational substrate of modern ML.

For a small example, move the point (1, 0) by a 90-degree rotation matrix. Multiply matrix by vector, track dimensions, and interpret the result geometrically rather than as symbol pushing. This is the mechanism to keep in view as the lesson becomes more technical. Before moving on, identify the input, transformation, output, and one observation that would falsify your conclusion.

Key points

Vectors, norms, dot products, angles, bases, and linear maps.
Matrix multiplication, rank, inverses, null spaces, and projections.
Eigenvalues, eigenvectors, determinants, and positive definiteness.

Use it well

When Linear Algebra helps—and where it breaks

A dataset has many redundant sensor readings. Center the matrix, inspect singular values, project to principal directions, and measure retained variance. A useful result still depends on checking the assumptions and evidence below rather than treating one successful output as proof.

Key points

Treating matrices as tables without geometry. Better approach: Connect every operation to a transformation, projection, or bilinear form.
Ignoring ill-conditioning. Better approach: Inspect singular values and use stable decompositions or regularization.
Optimizing FLOPs while ignoring data movement. Better approach: Profile memory layout and bandwidth on target hardware.

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