Index Symbols | A | B | C | D | E | F | G | H | I | L | M | N | O | P | Q | R | S | T | U | V | W | Z Symbols $i$-th component $i$-th entry $LU$ decomposition (main diagonal A a.m. adjugate matrix algebraic multiplicity, [1] angle associated homogeneous system asymptotically stable attractor, [1] augmented matrix B band matrix basic properties of a singular value decomposition. basic variables basis bijective C Cartesian equation, [1] Cauchy-Schwarz inequality Cayley-Hamilton center point change-of-coordinates matrix from ${\mathcal B}$ to ${\mathcal C}$ change-of-coordinates matrix from ${\mathcal B}$ to ${\mathcal E}$ characteristic polynomial classification of quadratic forms coefficient matrix coefficients, [1] cofactor cofactor matrix column space column vector columns complex conjugate, [1] complex diagonalizable complex number complex plane component functions components computing the singular values consistent constant term converges coordinate vector of $\vect{v}$ with respect to the basis $\mc{B}$ coordinates of the vector $\vect{v}$ with respect to the basis $\mc{B}$ Cramer's rule cross product D defect derivative determinant, [1], [2], [3] diagonal elements diagonal matrix diagonalizable diagonalization, [1] dimension dimension theorem directional vector, [1], [2] discrete dynamical system distance dominant eigenvalue dominant eigenvector dot product dynamical system E eigenspace eigenvalue eigenvector elementary matrices elementary row operations entries equal equality of matrices equivalent errors Euler's formula existence of a $PLU$ decomposition existence of a singular value decomposition F free variables fundamental theorem of algebra G g.m. general solution, [1], [2], [3] geometric multiplicity H homogeneous how row operations affect a determinant I identity matrix imaginary part imaginary unit in reduced echelon form inconsistent indefinite initial state initial values injective inner product inverse inverse power method L leading entry least squares error least squares solution linear linear $n$th order difference equation linear combination linear equation linear model linear system linear transformation linearly dependent linearly independent lower triangular matrices M Markov chain matrix matrix of $T$ with respect to bases $\mc{B}$ and $\mc{C}$ matrix transformation multiple multiplicity N negative definite negative semi-definite negatively oriented, [1] nonnegative norm normal normal equation, [1] normal equations normal vector, [1] null space O one-to-one orientation in $\R^n$ orthogonal, [1], [2] orthogonal basis orthogonal complement orthogonal projection orthogonal projection of a vector $\mathbf{w}$ onto the nonzero vector $\mathbf{v}$ orthonormal P parametric vector equation, [1], [2] path permutation matrix Perron-Frobenius pivot polar form positive definite positive definite matrix positive semi-definite positively oriented, [1] probability vector projection properties of the matrix $A^TA$ Q qr decomposition quadratic form under a substitution R rank rank theorem real part reduced echelon matrix reflection regular, [1] repeller, [1] represents rotation row echelon form row echelon matrix row equivalent row space row-column rule rows S saddle point, [1] scalar multiple, [1] scalar multiplication scalars scaling shear, [1] shear transformation, [1] shifted power method, [1] similar singular singular value decomposition singular values sink size, [1] solution, [1] solution set source span spectral decomposition of symmetric matrices spectral theorem, alternative version square matrix stable stable node stable spiral point standard basis, [1] standard matrix state vectors steady state stochastic matrix strictly smaller submatrix subspace sum, [1] surjective symmetric matrix system of differential equations system of $m$ equations in $n$ unknowns system of linear differential equations system of linear equations T test title the matrix of $T$ with respect to basis $\mathcal{B}$ the sum of two matrices thinning and extending trace trajectory transpose triangular matrix tridiagonal trivial subspaces U unit vector unit vector in the direction of $\mathbf{v}$ unknowns unstable unstable node unstable spiral point upper triangular matrix V vector vector-valued function volume volume in $\R^n$ W width Z zero matrix
