Vector v: (1.00, 1.00)
Transformed T(v): (3.00, 1.00)
Eigen-lines: 2 Real
a (îx): 2.0
b (ĵx): 1.0
c (îy): 0.0
d (ĵy): 1.0
Socratic Math Dialogue
Computed Spectral Properties
Eigenvalues (λ):
λ1 = 2.00, λ2 = 1.00
Eigenvectors (v):
[1, 0], [1, -1]
Span Invariance:
Span Preserved on 2 Lines
Canonical Proof & Discovery Summary
Horizontal Shear preserves vector direction along the x-axis (y = 0)
Under matrix T = [[2, 1], [0, 1]], vectors on the span of [1, 0] scale by eigenvalue λ = 2 without changing direction.
Socratic Mastery Level
Intuition Unlocked