Area model
A square of side a plus b is cut into its four partial areas, the two cross terms taking the emphasis, then collects back into one whole square.
CSS
Algebra
15 animationsCosets
A ring of twelve elements separates into three equal blocks that slide apart, each block the same subgroup shifted, then closes back into the whole group.
CSSCyclic group
A generator steps a marker around six ordered elements by one constant rotation at a time, dragging its orbit behind it and closing exactly on the identity.
CSSDeterminant
Two column vectors span a parallelogram whose area is the determinant; the second column swings across the first, collapsing the area to a line as the value passes through zero.
CSSDiagonalisation
The off-diagonal entries of a matrix clear from the far corners inward until only the leading diagonal is left carrying the weight.
CSSDifference of squares
A square notch is taken out of a larger square and the remaining piece swings a quarter turn to close the figure into the rectangle a plus b by a minus b.
CSSEigenvector
A fan of directions is swung by a linear map while one direction holds its own line and only stretches along it.
CSSFactor pair
A rectangle of constant area steps through its factor pairs, the corner walking the divisor lattice and landing exactly on each whole-number mark.
CSSMatrix product
A row of one matrix and a column of another are held together and the product cell they address fills, the pair walking every cell of the result in turn.
CSSOrthogonal projection
A vector swings above a subspace line while the perpendicular dropped from it keeps its right angle and the projection on the line lengthens and shortens.
CSSRing ideal
Elements multiplied in from three sides of a ring all land inside the same inner set, which absorbs them and stays closed.
CSSRotation matrix
An orthogonal frame turns through a fixed angle and back, lengths and the right angle held throughout while the swept arc measures the turn.
CSSRow reduction
A pivot box steps down the leading diagonal of an augmented matrix and every entry below it collapses away, leaving the array upper-triangular.
CSSShear map
A square grid leans into a parallelogram grid while the base row holds still, the unit cell keeping its area and losing its right angles.
CSSTranspose
Off-diagonal entries of a matrix cross the leading diagonal to their mirrored cells and back, while the diagonal itself never moves.
CSS