01 / FACTOR↘
LU
Break a square matrix into a lower and upper triangular pair. Partial pivoting keeps the path numerically honest.
solve · det · inverse
FROM-SCRATCH NUMERICS 01 / 04
See the machinery
behind the matrix.
A hands-on microscope for the algorithms behind linear algebra. Change a number, run the decomposition, and follow the structure all the way down.
09core routines
0black boxes
∞ways to perturb
LIVE INSTRUMENTMATRIX / 2×2 / 001
∷
A / INPUT MATRIX
det(A)10.000
A−1
[ 0.400 -0.200 ] [−0.100 0.300 ]
partial pivotingε < 1e−12
The fastest way to understand an algorithm is to make it misbehave.
A. Every output is inspectable
B. Every input is yours to change
C. Every method has a story
02INTERACTIVE LABEDIT / RUN / INSPECT
Put the numbers
under pressure.
Start with a preset or make your own small matrix. The lab favors readable intermediate results over a single mysterious answer.
INPUT / A3 × 3
Click any cell to edit
OUTPUT / TRACEREADY
03FIELD NOTESTHE METHOD MAP
Seven ways to
move information.
Decomposition is not just a computational trick. It is a decision about which structure you want to make visible.
02 / REFLECT↗
QR
Householder reflections turn a messy matrix into orthogonal directions and a triangular remainder.
stable least squares
03 / LISTEN◌
Eigen
For symmetric matrices, Jacobi rotations reveal the directions that remain themselves after transformation.
values · vectors
04 / COMPRESS⊙
SVD
Every matrix has a set of singular directions. The spectrum tells you what survives, what fades, and what can be compressed.
U · Σ · Vᵀ
05 / FIT⌁
Least squares
When no exact answer exists, find the one with the smallest residual and keep the error visible.
QR · regression
06 / REDUCE⌗
PCA
Rotate a cloud of observations toward the directions where its variance is doing the most work.
covariance · variance
07 / MODEL⌁
Polynomial fit
Use the least-squares machinery to recover a simple curve from noisy observations.
degree 2 · noise
04SOURCE REFERENCEPURE PYTHON / NO NUMPY
Read the original
instrument panel.
The browser lab is a visual companion. The source stays small enough to read in one sitting and honest enough to tinker with.
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