>We’re getting organized: inputs in vertical columns, operations in horizontal rows.
OH! Bloody hell, so that's why we write it like that!
>The eigenvector and eigenvalue represent the “axes” of the transformation.
>Consider spinning a globe: every location faces a new direction, except the poles.
>An “eigenvector” is an input that doesn’t change direction when it’s run through the matrix (it points “along the axis”). And although the direction doesn’t change, the size might. The eigenvalue is the amount the eigenvector is scaled up or down when going through the matrix.
Very nice! I'd had an algebraic (ahaha) understanding of eigenvectors/values before, but hadn't a geometric intuition. Thank you. Now I can neatly imagine why the eigenvector is orthogonal/perpendicular to the "direction" of the transformation.
OH! Bloody hell, so that's why we write it like that!
>The eigenvector and eigenvalue represent the “axes” of the transformation.
>Consider spinning a globe: every location faces a new direction, except the poles.
>An “eigenvector” is an input that doesn’t change direction when it’s run through the matrix (it points “along the axis”). And although the direction doesn’t change, the size might. The eigenvalue is the amount the eigenvector is scaled up or down when going through the matrix.
Very nice! I'd had an algebraic (ahaha) understanding of eigenvectors/values before, but hadn't a geometric intuition. Thank you. Now I can neatly imagine why the eigenvector is orthogonal/perpendicular to the "direction" of the transformation.
Determinants, too.
Excellent article.