matht.rip Linear Algebra Understanding Linear Algebra, all seven chapters

Drag to turn the globe. ←/→ or A/D step through the sections in order, ↑/↓ or W/S jump a chapter, and Enter sails there and opens it.

Section numbers, terms and most worked examples follow Understanding Linear Algebra and its Activity Workbook by David Austin (CC BY 4.0). Every section of the book has a tutorial and practice here; some titles are shortened, and each tutorial gives the book's own. Tutorials and practice problems are written for this site.

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    • Vectors: v = (2, 1). A named vector is an arrow; an unnamed pair like (3, 1) is a point.
    • Matrices: A = [[1, 2], [0, 1]] or [1, 2; 0, 1]. A 2 × 2 matrix is drawn as its transformation: the new grid, the image of the unit square (its area is |det A|), and the image of the unit circle.
    • Lines: 2x + y = 4 or y = 3x − 1. Crossings are marked and listed.
    • Sliders: a = 2, then use a anywhere, as in (a, 1) or y = a x.
    • Arithmetic: 2v − w, A v, A B, A^2, A^-1, A^T.
    • Functions: det(A), inv(A), eig(A), rref(A), dot(u, v), cross(u, v), norm(v), proj(b, w), span(u, v), rot(90) (a rotation, in degrees).
    • Space: vectors with three entries like (1, 2, 2), 3 × 3 matrices (drawn as the image of the unit cube) and planes like x + 2y − z = 1 switch the graph to 3D. Drag to turn it. The 3D button shows space for flat things too.
    • Far crossings: when two lines meet far away, an arrow at the edge of the graph shows where, and clicking it goes there. The ⋯ menu can make Fit always include far crossings, or stretch the axes so x and y have separate scales.
    • When things overlap: labels move out of each other's way, and equal vectors share one label (v, A v). Drawn twice, an equal line or arrow is dashed so both colours show. Point at a spot to list everything there, and click a row's dot to hide it.
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