Mathematics Hub/Linear Algebra Matrix Transformation Arena

Linear Algebra Matrix Transformation Arena

Visualize 2D linear vector space transformations T(v) = Av, real-time determinant area scaling, and eigenvector invariant axes.

A = [ 1.50, 0.50 ; 0.50, 1.20 ]

Area Scale Factor: |det(A)| = 1.550

? T(?) = [1.5, 0.5]? T(?) = [0.5, 1.2]? Eigenvector Axis

a (x ? x):

b (y ? x):

c (x ? y):

d (y ? y):

Determinant det(A):1.550

Trace tr(A) = a + d:2.700

Eigenvalues (??, ??):1.872, 0.828

Axes where vectors undergo pure scaling without rotation.

Inverse Matrix A??:

[ 0.77, -0.32 ; -0.32, 0.97 ]

Loading NexProTools...

Preparing interactive calculation engine