docs(matrices): fix references and add DOIs

src/matrices/binomial.jl

@@ -7,8 +7,9 @@ The matrix is a multiple of an involutory matrix.
 - dim: the dimension of the matrix.
 
 # References
-**G. Boyd, C.A. Micchelli, G. Strang and D.X. Zhou**,
-Binomial matrices, Adv. in Comput. Math., 14 (2001), pp 379-391.
+**G. Boyd, C. A. Micchelli, G. Strang and D. X. Zhou**,
+Binomial matrices, Adv. Comput. Math., 14 (2001), pp. 379-391,
+https://doi.org/10.1023/A:1012207124894.
 """
 struct Binomial{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/cauchy.jl

@@ -12,8 +12,9 @@ Given two vectors `x` and `y`, the `(i,j)` entry of the Cauchy matrix is
 
 # References
 **N. J. Higham**, Accuracy and Stability of Numerical Algorithms,
-second edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA,
-2002; sec. 28.1
+second edition, Society for Industrial and Applied Mathematics,
+Philadelphia, PA, USA, 2002, https://doi.org/10.1137/1.9780898718027.
+See sect. 28.1.
 """
 struct Cauchy{T<:Number,X<:AbstractVector,Y<:AbstractVector} <: AbstractMatrix{T}
     x::X

src/matrices/chebspec.jl

@@ -13,7 +13,8 @@ If `k = 0`,the generated matrix is nilpotent and a vector with
 
 # References
 **L. N. Trefethen and M. R. Trummer**, An instability
-        phenomenon in spectral methods, SIAM J. Numer. Anal., 24 (1987), pp. 1008-1023.
+phenomenon in spectral methods, SIAM J. Numer. Anal., 24 (1987),
+pp. 1008-1023, https://doi.org/10.1137/0724066.
 """
 struct ChebSpec{T<:Number} <: AbstractMatrix{T}
     n::Int

src/matrices/chow.jl

@@ -11,7 +11,8 @@ The Chow matrix is a singular Toeplitz lower Hessenberg matrix.
 
 # References
 **T. S. Chow**, A class of Hessenberg matrices with known
-                eigenvalues and inverses, SIAM Review, 11 (1969), pp. 391-395.
+eigenvalues and inverses, SIAM Rev., 11 (1969), pp. 391-395,
+https://doi.org/10.1137/1011065.
 """
 struct Chow{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/clement.jl

@@ -11,8 +11,9 @@ The Clement matrix is a tridiagonal matrix with zero
 - dim: `k = 0`.
 
 # References
-**P. A. Clement**, A class of triple-diagonal
-        matrices for test purposes, SIAM Review, 1 (1959), pp. 50-52.
+**P. A. Clement**, A class of triple-diagonal matrices
+for test purposes, SIAM Rev., 1 (1959), pp. 50-52,
+https://doi.org/10.1137/1001006.
 """
 abstract type Clement{T<:Number} <: AbstractMatrix{T} end
 

src/matrices/companion.jl

@@ -11,7 +11,12 @@ The companion matrix to a monic polynomial
 # Input Options
 - vec: `vec` is a vector of coefficients.
 - dim: `vec = [1:dim;]`. `dim` is the dimension of the matrix.
-- polynomial: `polynomial` is a polynomial. vector will be appropriate values from coefficients.
+- polynomial: `polynomial` is a polynomial. Last column will contain
+its coefficients.
+
+# References
+**N. J. Higham**, What Is the Companion Matrix?,
+https://nhigham.com/2021/03/23/what-is-a-companion-matrix/
 """
 struct Companion{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/comparison.jl

@@ -8,6 +8,10 @@ The comparison matrix for another matrix.
     `k = 0`: each element is absolute value of `B`, except each diagonal element is negative absolute value.
     `k = 1`: each diagonal element is absolute value of `B`, except each off-diagonal element is negative largest absolute value in the same row.
 - B: `B` is a matrix and `k = 1`.
+
+**N. J. Higham**, Efficient algorithms for computing the condition number
+of a tridiagonal matrix, SIAM J. Sci. Stat. Comput., 7 (1986), pp. 150-165, 
+https://doi.org/10.1137/0907011.
 """
 struct Comparison{T<:Number} <: AbstractMatrix{T}
     A::AbstractMatrix{T}

src/matrices/dingdong.jl

@@ -9,9 +9,9 @@ The eigenvalues cluster around `π/2` and `-π/2`.
 - dim: the dimension of the matrix.
 
 # References
-**J. C. Nash**, Compact Numerical Methods for
-Computers: Linear Algebra and Function Minimisation,
-second edition, Adam Hilger, Bristol, 1990 (Appendix 1).
+**J. C. Nash**, Compact Numerical Methods for Computers:
+Linear Algebra and Function Minimisation, second edition,
+Adam Hilger, Bristol, 1990 (Appendix 1).
 """
 struct DingDong{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/fiedler.jl

@@ -9,11 +9,11 @@ The Fiedler matrix is symmetric matrix with a dominant
 - dim: `dim` is the dimension of the matrix. `vec=[1:dim;]`.
 
 # References
-**G. Szego**, Solution to problem 3705, Amer. Math.
-            Monthly, 43 (1936), pp. 246-259.
+**A. C. Schaeffer and G. Szegö**, Solution to problem 3705, Amer. Math. Monthly,
+43 (1936), pp. 246-259, https://doi.org/10.1090/S0002-9947-1941-0005164-7.
 
 **J. Todd**, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
-            Birkhauser, Basel, and Academic Press, New York, 1977, p. 159.
+Birkhauser, Basel, and Academic Press, New York, 1977, p. 159.
 """
 struct Fiedler{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/frank.jl

@@ -11,9 +11,10 @@ very ill conditioned.
 - dim: the dimension of the matrix.
 
 # References
-**W. L. Frank**, Computing eigenvalues of complex matrices
-    by determinant evaluation and by methods of Danilewski and Wielandt,
-    J. Soc. Indust. Appl. Math., 6 (1958), pp. 378-392 (see pp. 385, 388).
+**W. L. Frank**, Computing eigenvalues of complex matrices by determinant
+evaluation and by methods of Danilewski and Wielandt, J. Soc. Indust.
+Appl. Math., 6 (1958), pp. 378-392, https://doi.org/10.1137/0106026.
+See pp. 385 and 388.
 """
 struct Frank{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/gearmat.jl

@@ -8,6 +8,11 @@ other elements are 0.
 # Input Options
 - dim: the dimension of the matrix. `i = n` and `j = -n` by default.
 - dim, i, j: the dimension of the matrix and the position of the 1's.
+
+# References
+**C. W. Gear**, A simple set of test matrices for eigenvalue programs,
+Math. Comp., 23 (1969), pp. 119-125,
+https://doi.org/10.1090/S0025-5718-1969-0238477-8.
 """
 struct GearMat{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/golub.jl

@@ -9,9 +9,9 @@ Golub matrix is the product of two random unit lower and upper
 - dim: the dimension of the matrix.
 
 # References
-**D. Viswanath and N. Trefethen**. Condition Numbers of
-    Random Triangular Matrices, SIAM J. Matrix Anal. Appl. 19, 564-581,
-    1998.
+**D. Viswanath and N. Trefethen**. Condition numbers of random
+triangular matrices, SIAM J. Matrix Anal. Appl., 19 (1998), 564-581,
+https://doi.org/10.1137/S0895479896312869.
 """
 struct Golub{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/grcar.jl

@@ -10,9 +10,9 @@ eigenvalues.
 - dim: the dimension of the matrix.
 
 # References
-**J. F. Grcar**, Operator coefficient methods
-    for linear equations, Report SAND89-8691, Sandia National
-    Laboratories, Albuquerque, New Mexico, 1989 (Appendix 2).
+**J. F. Grcar**, Operator coefficient methods for linear equations,
+Report SAND89-8691, Sandia National Laboratories, Albuquerque,
+New Mexico, 1989 (Appendix 2).
 """
 struct Grcar{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/hadamard.jl

@@ -9,8 +9,9 @@ a Hadamard matrix are orthogonal.
 - dim: the dimension of the matrix, `dim` is a power of 2.
 
 # References
-**S. W. Golomb and L. D. Baumert**, The search for
-Hadamard matrices, Amer. Math. Monthly, 70 (1963) pp. 12-17
+**S. W. Golomb and L. D. Baumert**, The search for Hadamard
+matrices, Amer. Math. Monthly, 70 (1963) pp. 12-17,
+https://doi.org/10.1080/00029890.1963.11990035.
 """
 struct Hadamard{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/hilbert.jl

@@ -13,11 +13,12 @@ See also [`InverseHilbert`](@ref).
 
 # References
 **M. D. Choi**, Tricks or treats with the Hilbert matrix,
-Amer. Math. Monthly, 90 (1983), pp. 301-312.
+Amer. Math. Monthly, 90 (1983), pp. 301-312,
+https://doi.org/10.1080/00029890.1983.11971218.
 
 **N. J. Higham**, Accuracy and Stability of Numerical Algorithms,
 second edition, Society for Industrial and Applied Mathematics,
-Philadelphia, PA, USA, 2002; sec. 28.1.
+Philadelphia, PA, USA, 2002. See sect. 28.1.
 """
 struct Hilbert{T<:Number} <: AbstractMatrix{T}
     m::Integer

src/matrices/inversehilbert.jl

@@ -9,11 +9,12 @@ See also [`Hilbert`](@ref).
 
 # References
 **M. D. Choi**, Tricks or treats with the Hilbert matrix,
-    Amer. Math. Monthly, 90 (1983), pp. 301-312.
+Amer. Math. Monthly, 90 (1983), pp. 301-312,
+https://doi.org/10.1080/00029890.1983.11971218.
 
 **N. J. Higham**, Accuracy and Stability of Numerical Algorithms, second
-    edition, Society for Industrial and Applied Mathematics, Philadelphia, PA,
-    USA, 2002; sec. 28.1.
+edition, Society for Industrial and Applied Mathematics, Philadelphia, PA,
+USA, 2002. See sect. 28.1.
 """
 struct InverseHilbert{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/involutory.jl

@@ -7,9 +7,9 @@ An involutory matrix is a matrix that is its own inverse.
 - dim: `dim` is the dimension of the matrix.
 
 # References
-**A. S. Householder and J. A. Carpenter**, The
-        singular values of involutory and of idempotent matrices,
-        Numer. Math. 5 (1963), pp. 234-237.
+**A. S. Householder and J. A. Carpenter**, The singular values
+of involutory and of idempotent matrices, Numer. Math. 5 (1963),
+pp. 234-237, https://doi.org/10.1007/BF01385894.
 """
 struct Involutory{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/kahan.jl

@@ -13,8 +13,8 @@ The Kahan matrix is an upper trapezoidal matrix, i.e., the
 - dim: `θ = 1.2`, `pert = 25`.
 
 # References
-**W. Kahan**, Numerical linear algebra, Canadian Math.
-    Bulletin, 9 (1966), pp. 757-801.
+**W. Kahan**, Numerical linear algebra, Canadian Math. Bulletin,
+9 (1966), pp. 757-801, https://doi.org/10.4153/CMB-1966-083-2.
 """
 struct Kahan{T<:Number} <: AbstractMatrix{T}
     m::Integer

src/matrices/kms.jl

@@ -8,9 +8,12 @@ Kac-Murdock-Szego Toeplitz matrix
 - dim: `rho = 0.5`.
 
 # References
-**W. F. Trench**, Numerical solution of the eigenvalue
-    problem for Hermitian Toeplitz matrices, SIAM J. Matrix Analysis
-    and Appl., 10 (1989), pp. 135-146 (and see the references therein).
+**W. F. Trench**, Numerical solution of the eigenvalue problem for Hermitian
+Toeplitz matrices, SIAM J. Matrix Anal. Appl., 10 (1989), pp. 135-146,
+https://doi.org/10.1137/0610010.
+
+**N. J. Higham**, What Is the Kac-Murdock-Szegö Matrix?,
+https://nhigham.com/2021/07/06/what-is-the-kac-murdock-szego-matrix/
 """
 struct KMS{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/lehmer.jl

@@ -9,11 +9,14 @@ The Lehmer matrix is a symmetric positive definite matrix.
 - dim: the dimension of the matrix.
 
 # References
-**M. Newman and J. Todd**, The evaluation of
-            matrix inversion programs, J. Soc. Indust. Appl. Math.,
-            6 (1958), pp. 466-476.
-            Solutions to problem E710 (proposed by D.H. Lehmer): The inverse
-            of a matrix, Amer. Math. Monthly, 53 (1946), pp. 534-535.
+**M. Newman and J. Todd**, The evaluation of matrix inversion programs,
+J. Soc. Indust. Appl. Math., 6 (1958), pp. 466-476, https://doi.org/10.1137/0106030.
+
+**D. H. Lehmer**, Problem E710: The inverse of a matrix,
+Amer. Math. Monthly, 53 (1946), p. 97, https://doi.org/10.2307/2305463.
+
+Solutions by D. M. Smiley and M. F. Smiley, and by John Williamson.
+Amer. Math. Monthly, 53 (1946), pp. 534-535, https://doi.org/10.2307/2305078.
 """
 struct Lehmer{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/lotkin.jl

@@ -9,7 +9,8 @@ The Lotkin matrix is the Hilbert matrix with its first row
 - dim: `dim` is the dimension of the matrix.
 
 # References
-**M. Lotkin**, A set of test matrices, MTAC, 9 (1955), pp. 153-161.
+**M. Lotkin**, A set of test matrices, Math. Tables Aid Comput.,
+9 (1955), pp. 153-161, https://doi.org/10.2307/2002051.
 """
 struct Lotkin{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/minij.jl

@@ -9,9 +9,9 @@ A matrix with `(i,j)` entry `min(i,j)`. It is a symmetric positive
 - dim: the dimension of the matrix.
 
 # References
-**J. Fortiana and C. M. Cuadras**, A family of matrices,
-            the discretized Brownian bridge, and distance-based regression,
-            Linear Algebra Appl., 264 (1997), 173-188.  (For the eigensystem of A.)
+**J. Fortiana and C. M. Cuadras**, A family of matrices, the discretized
+Brownian bridge, and distance-based regression, Linear Algebra Appl.,
+264 (1997), pp. 173-188, https://doi.org/10.1016/S0024-3795(97)00051-7.
 """
 struct Minij{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/moler.jl

@@ -11,8 +11,8 @@ It has one small eigenvalue.
 
 # References
 **J.C. Nash**, Compact Numerical Methods for Computers:
-    Linear Algebra and Function Minimisation, second edition,
-    Adam Hilger, Bristol, 1990 (Appendix 1).
+Linear Algebra and Function Minimisation, second edition,
+Adam Hilger, Bristol, 1990 (Appendix 1).
 """
 struct Moler{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/neumann.jl

@@ -8,8 +8,8 @@ A singular matrix from the discrete Neumann problem.
 - dim: the dimension of the matrix, must be a perfect square integer.
 
 # References
-**R. J. Plemmons**, Regular splittings and the
-          discrete Neumann problem, Numer. Math., 25 (1976), pp. 153-161.
+**R. J. Plemmons**, Regular splittings and the discrete Neumann problem,
+Numer. Math., 25 (1976), pp. 153-161, https://doi.org/10.1007/BF01462269.
 """
 struct Neumann{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/oscillate.jl

@@ -13,9 +13,9 @@ A matrix `A` is called oscillating if `A` is totally
 - dim: `mode = 1`.
 
 # References
-**Per Christian Hansen**, Test matrices for
-    regularization methods. SIAM J. SCI. COMPUT Vol 16,
-    No2, pp 506-512 (1995).
+**P. C. Hansen**, Test matrices for regularization methods, SIAM J.
+Sci. Comput., 16 (1995), pp. 506-512, https://doi.org/10.1137/0916032.
+.
 """
 struct Oscillate{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/parter.jl

@@ -8,10 +8,11 @@ The Parter matrix is a Toeplitz and Cauchy matrix
 - dim: the dimension of the matrix.
 
 # References
-The MathWorks Newsletter, Volume 1, Issue 1,
-            March 1986, page 2. S. V. Parter, On the distribution of the
-            singular values of Toeplitz matrices, Linear Algebra and
-            Appl., 80 (1986), pp. 115-130.
+The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2.
+
+**S. V. Parter**, On the distribution of the singular values of
+Toeplitz matrices, Linear Algebra Appl., 80 (1986), pp. 115-130,
+https://doi.org/10.1016/0024-3795(86)90280-6.
 """
 struct Parter{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/pascal.jl

@@ -14,7 +14,7 @@ The Pascal matrix’s anti-diagonals form the Pascal’s triangle.
 
 **N. J. Higham**, Accuracy and Stability of Numerical Algorithms,
 second edition, Society for Industrial and Applied Mathematics, Philadelphia, PA,
-USA, 2002; sec. 28.4.
+USA, 2002. See sect. 28.4.
 """
 struct Pascal{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/pei.jl

@@ -10,7 +10,7 @@ The Pei matrix is a symmetric matrix with known inversion.
 
 # References
 **M. L. Pei**, A test matrix for inversion procedures,
-    Comm. ACM, 5 (1962), p. 508.
+Comm. ACM, 5 (1962), p. 508, https://doi.org/10.1145/368959.368975.
 """
 struct Pei{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/poisson.jl

@@ -10,8 +10,8 @@ A block tridiagonal matrix from Poisson’s equation.
 
 # References
 **G. H. Golub and C. F. Van Loan**, Matrix Computations,
-          second edition, Johns Hopkins University Press, Baltimore,
-          Maryland, 1989 (Section 4.5.4).
+second edition, Johns Hopkins University Press, Baltimore,
+Maryland, 1989. See sect. 4.5.4.
 """
 struct Poisson{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/prolate.jl

@@ -8,8 +8,8 @@ A prolate matrix is a symmetirc, ill-conditioned Toeplitz matrix.
 - dim: the case when `w = 0.25`.
 
 # References
-**J. M. Varah**. The Prolate Matrix. Linear Algebra and Appl.
-             187:267--278, 1993.
+**J. M. Varah**. The Prolate matrix. Linear Algebra Appl., 187 (1993),
+pp. 267-278, https://doi.org/10.1016/0024-3795(93)90142-B.
 """
 struct Prolate{T<:Number} <: AbstractMatrix{T}
     n::Integer

src/matrices/randsvd.jl

@@ -17,7 +17,7 @@ Random Matrix with Pre-assigned Singular Values
 # References
 **N. J. Higham**, Accuracy and Stability of Numerical
 Algorithms, second edition, Society for Industrial and Applied Mathematics,
-Philadelphia, PA, USA, 2002; sec. 28.3.
+Philadelphia, PA, USA, 2002. See sect. 28.3.
 """
 struct RandSVD{T<:Number} <: AbstractMatrix{T}
     m::Integer

src/matrices/rohess.jl

@@ -7,8 +7,9 @@ The matrix is constructed via a product of Givens rotations.
 - dim: the dimension of the matrix.
 
 # References
-**W. B. Gragg**, The QR algorithm for unitary
-    Hessenberg matrices, J. Comp. Appl. Math., 16 (1986), pp. 1-8.
+**W. B. Gragg**, The QR algorithm for unitary Hessenberg matrices,
+J. Comp. Appl. Math., 16 (1986), pp. 1-8,
+https://doi.org/10.1016/0377-0427(86)90169-X.
 """
 struct Rohess{T<:Number} <: AbstractMatrix{T}
     n::Integer