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 $QR$ decomposition A 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 centre centre 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 cofactor cofactor matrix column echelon matrix column space column vector columns complex conjugate, [1] complex diagonalisable complex diagonalisation complex number complex plane component functions components computing the sngular 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 matrix derivative determinant, [1], [2], [3] diagonal diagonal elements diagonal matrix diagonalisable diagonalisation dimension dimension theorem directional vector, [1], [2] discrete dynamical system distance dominant eigenvalue dominant eigenvector dot product dynamical system E echelon form eigenfunction 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 flow map free variables fundamental theorem of algebra G general solution geometric multiplicity H homogeneous how row operations affect a determinant I identity matrix imaginary part imaginary unit in reduced echelon form inconsistent indefinite quadratic form initial values injective inner product inverse inverse power method invertible L leading entry least-squares error least-squares solution linear linear $n$-th order difference equation linear combination, [1] linear equation linear model linear system linear transformation linearly dependent linearly dependent on linearly independent, [1] lower-triangular matrices M main diagonal 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 orientated, [1] norm normal equation, [1] normal equations normal vector, [1] null space O one-to-one onto orientation in $\R^n$ orthogonal, [1] orthogonal basis orthogonal complement orthogonal matrix orthogonal projection, [1] orthonormal P parametric vector equation, [1], [2] path permutation matrix Perron-Frobenius pivot polar form positive definite matrix positive definite quadratic form positive semi-definite positively orientated, [1] probability vector projection properties of the matrix $A^TA$ Q quadratic form under a substitution R rank rank theorem real part reduced echelon matrix reflection regular regular matrix 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, [1] shear, [1] shear transformation, [1] shifted inverse power method shifted power method similar singular matrix singular value decomposition singular values sink size, [1], [2] skew-symmetric solution, [1] solution set source span spectral decomposition of symmetric matrices spectral theorem, alternative version square matrix stable stable node stable spiral point, [1] standard basis, [1] standard matrix state vectors steady state stochastic matrix 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 the matrix of $T$ with respect to basis $\mathcal{B}$ the sum of two matrices thinning and extending trace trajectory, [1] transpose triangular matrix tridiagonal trivial subspaces U unit vector unknowns unstable unstable node unstable spiral point, [1] upper-triangular matrix V vector vector-valued function volume volume in $\R^n$ W width Z zero matrix
