The computation lab¶
Here you do not only get the answer: you see every step, written the way you would write it by hand, with the notation of the lecture notes (\(R_2 \leftarrow R_2 - 2R_1\)). The arithmetic is exact: fractions, never rounded decimals. Pick a tool: each one opens full page, with tabs to compute, to practice on exercises generated for you, and (for Gaussian elimination) to do it yourself, choosing each row operation.
Everything runs in your browser: nothing to install, no account, and it works on a phone.
Sums and products (chapters 1–2)¶
-
Sums and products
Expands \(\sum\) and \(\prod\) and compares them with the closed formulas of the notes.
Vectors and matrices (chapters 3–4)¶
-
Matrix product
Row by column, one entry at a time.
-
Rank
The rank as the number of pivots of the row echelon form.
-
Determinant
Laplace expansion, Sarrus rule or Gaussian elimination, your choice.
-
Gaussian elimination
Bring a matrix to row echelon (or reduced) form showing every elementary operation.
-
Why partial pivoting
The same system with and without partial pivoting, in floating point.
-
Inverse matrix
Gauss–Jordan on \((\boldsymbol A \mid \boldsymbol I)\) or the cofactor formula.
-
LU factorization
The multipliers that fill \(\boldsymbol L\), the swaps that fill \(\boldsymbol P\).
-
Eigenvalues and definiteness
Characteristic polynomial, eigenvectors and Sylvester's criterion.
Norms (chapter 5)¶
-
Norms
The \(\ell_1\), \(\ell_2\), \(\ell_\infty\) norms and the one generalized by \(\boldsymbol Q\).
Linear systems (chapter 6)¶
-
Linear systems
Gauss and back substitution, Rouché–Capelli, Cramer, or the LU factorization.