https://www.quanty.org/ 2026-04-29T11:46:16+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T03:20:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/addspin?rev=1763608836&do=diff AddSpin Matrix.AddSpin($M$) takes a Matrix $M$ that acts on a space with no spin included and returns the matrix doubled in size, where every former entry now splits in spin-up and spin-down. We assume the ordering of the basis alternates between spin up and down. This behaviour is equivalent to calling matrix index text/html 2025-11-20T03:20:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/conjugate?rev=1763608836&do=diff Conjugate Matrix.Conjugate($M$) takes a matrix and returns it with every entry replaced by its complex conjugate. Example Input A = Matrix.New({{1,1+2*I},{3,4+I}}) B = Matrix.Conjugate(A) print(B) Result { { 1 , 1 - 2 I } , { 3 , 4 - 1 I } } matrix index text/html 2025-11-20T03:20:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/conjugatetranspose?rev=1763608840&do=diff ConjugateTranspose Matrix.ConjugateTranspose($M$) takes a matrix $M$ and returns its conjugate transpose. Example Input A = Matrix.New({{1,1+2*I},{3,4+I}}) B = Matrix.ConjugateTranspose(A) print(B) Result { { 1 , 3 } , { 1 - 2 I , 4 - 1 I } } matrix index text/html 2025-11-20T03:20:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/diagonal?rev=1763608841&do=diff Diagonal Matrix.Diagonal($\{x_1,x_2,...,x_n\}$) takes a list of $n$ numbers and returns an $n \times n$ diagonal matrix with the $x_i$ as entries. If the option “Userdata” is set to true (default is false) the output is returned as a pointer rather than a table of tables (compare Matrix.ToUserdata()). Example matrix index text/html 2025-11-20T03:20:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/eigensystem?rev=1763608838&do=diff Matrix.Eigensystem Matrix.Eigensystem(M) calculates the eigenvalues and eigenvectors of the square matrix M. If M is Hermitian it returns the eigenvalues and a single eigenvector, if M is non-hermitian it returns both the left and right eigenvectors matrix index text/html 2025-11-20T03:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/enlarge?rev=1763608837&do=diff Enlarge Matrix.Enlarge($M$,$n$) takes a Matrix $M$ and replaces every entry with a diagonal matrix of size $n$ and entries equal to the original entry. Compare Matrix.AddSpin(). Example Input M ={{3,5}, {-2,I}} print(Matrix.Enlarge(M,3)) Result { { 3 , 0 , 0 , 5 , 0 , 0 } , { 0 , 3 , 0 , 0 , 5 , 0 } , { 0 , 0 , 3 , 0 , 0 , 5 } , { -2 , 0 , 0 , (0 + 1 I) , 0 , 0 } , { 0 , -2 , 0 , 0 , (0 + 1 I) , 0 } , { 0 , 0 , -2 , 0 , 0 , (0 + 1 I) } } matrix index text/html 2025-11-20T03:20:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/exp?rev=1763608839&do=diff Exp Matrix.Exp($M$) takes $M$ and returns $e^M = \sum_{n=0}^{\infty} \frac{M^n}{n!}$. Example Input M ={{-10,1}, {1,0.3}} print(Matrix.Exp(M)) Result { { 0.013665171949002 , 0.14163701011454 } , { 0.14163701011454 , 1.4725263761288 } } Table of contents matrix index text/html 2025-11-20T03:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/expand?rev=1763608837&do=diff Expand Matrix.Expand($M$, $n$, $x$) takes a quadratic matrix $M$ of dimension $m$ by $m$ and enlarges the dimension to $n$ by $n$, with $n\geq m$ required. The new diagonal values are set to $x$. If $x$ is not given all new entries are set to 0. Example Input A = Matrix.New({{1,2}, {3,4}}) B = Matrix.Expand(A,4) C = Matrix.Expand(A,4,3) print(B) print(C) matrix index text/html 2025-11-20T03:20:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/flatten?rev=1763608838&do=diff Flatten Matrix.Flatten($M$) takes an object $M$, which must be a matrix with matrix-valued entries, and returns the flattened version, which is a matrix with numbers as entries. This allows for working with block matrices, e.g. defining a matrix of the form \begin{equation} M= \left( \begin{matrix} A & B \\ C & D\\ \end{matrix} \right) \end{equation}$A,B,C,D$$M$$0$matrix index text/html 2025-11-20T03:20:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/identity?rev=1763608841&do=diff Identity Matrix.Identity(n) returns an identity matrix of size $n\times n$. If the option “Userdata” is set to false (default is true) the output is returned as a table of tables rather than a pointer (compare Matrix.ToUserdata() and Matrix.ToTable()). Example Input print(Matrix.Identity(3)) matrix index text/html 2025-11-20T03:20:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/inverse?rev=1763608835&do=diff Inverse Matrix.Inverse($M$) returns $M^{-1}$. Example Input M = Matrix.New({{1,2},{2,1}}) Minv = Matrix.Inverse(M) print("The inverse of the matrix M") print(M) print("is") print(Minv) print("And Minv * M is") print(Minv*M) Result The inverse of the matrix M { { 1 , 2 } , { 2 , 1 } } is { { -0.3333 , 0.6667 } , { 0.6667 , -0.3333 } } And Minv * M is { { 1 , 0 } , { 0 , 1 } } matrix index text/html 2025-11-20T03:20:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/new?rev=1763608841&do=diff Matrix.New Matrix.New(T) creates a matrix object from the table t. Matrices can only have numerical (real or complex) entries and all rows must be of equal length. Example Input M = Matrix.New({{1,2},{2,1}}) print(M) Result { { 1 , 2 } , { 2 , 1 } } matrix index text/html 2025-11-20T03:20:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/random?rev=1763608839&do=diff Random Matrix.Random({$min$,$max$},{$m$,$n$}) returns a matrix of size $m \times n$ where every entry is a random number between $min$ and $max$. If the option “Userdata” is set to false (default is true) the output is returned as a table of tables rather than a pointer (compare Matrix.ToUserdata() and matrix index text/html 2025-11-20T03:20:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/removespin?rev=1763608836&do=diff RemoveSpin Matrix.RemoveSpin(M) removes all even columns and even rows of matrix M. Example Input M = Matrix.New({{1,0,2,0}, {0,1,0,2}, {3,0,4,0}, {0,3,0,4}}) S = Matrix.RemoveSpin(M) print(M) print(S) matrix index text/html 2025-11-20T03:20:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/rotate?rev=1763608835&do=diff Rotate Matrix.Rotate($M$,$U$) makes the matrix transformation $U^* . M . U^T$. Example Input M = Matrix.New({{ 1, I, 2, I}, {-I, 1, I, 2}, { 2,-I, 4, I}, {-I, 2,-I, 4}}) val, fun = Matrix.Eigensystem(M) Mdiag = Chop(Rotate(M,fun)) print(Mdiag) matrix index text/html 2025-11-20T03:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/sqrt?rev=1763608837&do=diff Sqrt Matrix.Sqrt($M$) takes a quadratic matrix $M$ and returns $\sqrt{M}$, which is defined by the property $\sqrt{M}\sqrt{M} = M$. M must be Hermitian and positive definite. Example Input M = {{1,2*I}, {-2*I,4}} print("M:") print(M) sqrtM = Matrix.Sqrt(M) print("sqrt(M):") print(sqrtM) print("sqrt(M)*sqrt(M)") print(sqrtM*sqrtM) matrix index text/html 2025-11-20T03:20:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/start?rev=1763608838&do=diff Functions Quanty defines a small library of functions that work on matrix objects. Available Functions functions index text/html 2025-11-20T03:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/sub?rev=1763608837&do=diff Sub Matrix.Sub($M$,$n$) takes a Matrix $M$ and returns the upper left submatrix of size $n\times n$. Matrix.Sub($M$,$r$,$c$) takes a Matrix $M$ and returns the upper left submatrix of size $r \times c$. Matrix.Sub($M$, $r_0$, $r$, $c_0$, $c$) takes a Matrix $M$ and returns a submatrix of size $r \times c$, where the $1,1$ element of the new matrix coincides with the $r_0,c_0$$M$$1$$0$matrix index text/html 2025-11-20T03:20:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/tooperator?rev=1763608840&do=diff ToOperator Matrix.Operator(M) creates an operator $O = \sum_{i,j} M[i][j] a^{\dagger}_{i-1} a_{j-1}^{\phantom{\dagger}}$ from the matrix $M$ Example Input M = {{1,2*I}, {-2*I,4}} O = Matrix.ToOperator(M) print(O) Result Operator: Operator QComplex = 1 (Real==0 or Complex==1 or Mixed==2) MaxLength = 2 (largest number of product of lader operators) NFermionic modes = 2 (Number of fermionic modes (site, spin, orbital, ...) in the one particle b… text/html 2025-11-20T03:20:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/totable?rev=1763608835&do=diff Matrix.ToTable Matrix.ToTable($M$) takes a matrix $M$ in userdata form and returns the object as a table of tables in lua. Compare Matrix.ToUserdata(). Table of contents matrix index text/html 2025-11-20T03:20:37+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/touserdata?rev=1763608837&do=diff Matrix.ToUserdata Matrices are, per default, tables of tables in Lua. When algebraic operations are performed on them, they are repeatedly copied and moved, which can lead to severe performance issues if the matrices are large objects. A call of Matrix.ToUserdata($M$matrix index text/html 2025-11-20T03:20:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/transpose?rev=1763608839&do=diff Transpose Matrix.Transpose($M$) takes a matrix $M$ and returns its transpose. Example Input A = Matrix.New({{1,1+2*I},{3,4+I}}) B = Matrix.Transpose(A) print(B) Result { { 1 , 3 } , { 1 + 2 I , 4 + 1 I } } matrix index text/html 2025-11-20T03:20:39+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/tridiagonalize?rev=1763608839&do=diff Tridiagonalize Matrix.Tridiagonalize(M) returns the matrix in triple-diagonal form. The first element returned is a try-diagonal response function representing the matrix. The second element returned is a matrix that represents the unitary matrix that transforms the Hermitian matrix M to try-diagonal form. Possible options includematrix index text/html 2025-11-20T03:20:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/matrix/functions/zero?rev=1763608835&do=diff Zero Matrix.Zero(n) returns a zero matrix of size $n\times n$. If the option “Userdata” is set to false (default is true) the output is returned as a table of table rather than a pointer (compare Matrix.ToUserdata() and Matrix.ToTable()). Example Input print(Matrix.Zero(3)) Result { { 0 , 0 , 0 } , { 0 , 0 , 0 } , { 0 , 0 , 0 } } matrix index