# Table of Contents - matrix: Ruby Standard Library Documentation

## Classes and Modules

- ExceptionForMatrix
- ExceptionForMatrix::ErrDimensionMismatch
- ExceptionForMatrix::ErrNotRegular
- ExceptionForMatrix::ErrOperationNotDefined
- ExceptionForMatrix::ErrOperationNotImplemented
- Matrix
- Matrix::EigenvalueDecomposition
- Matrix::LUPDecomposition
- Vector
  - Method Catalogue
- Vector::ZeroVectorError

## Methods

- ::I — Matrix
- ::[] — Matrix
- ::[] — Vector
- ::basis — Vector
- ::build — Matrix
- ::column_vector — Matrix
- ::columns — Matrix
- ::combine — Matrix
- ::diagonal — Matrix
- ::elements — Vector
- ::empty — Matrix
- ::hstack — Matrix
- ::identity — Matrix
- ::independent? — Vector
- ::new — ExceptionForMatrix::ErrDimensionMismatch
- ::new — ExceptionForMatrix::ErrNotRegular
- ::new — ExceptionForMatrix::ErrOperationNotDefined
- ::new — ExceptionForMatrix::ErrOperationNotImplemented
- ::new — Matrix
- ::new — Vector
- ::new — Matrix::EigenvalueDecomposition
- ::new — Matrix::LUPDecomposition
- ::row_vector — Matrix
- ::rows — Matrix
- ::scalar — Matrix
- ::unit — Matrix
- ::vstack — Matrix
- ::zero — Matrix
- ::zero — Vector
- #* — Matrix
- #* — Vector
- #** — Matrix
- #+ — Matrix
- #+ — Vector
- #+@ — Matrix
- #+@ — Vector
- #- — Matrix
- #- — Vector
- #-@ — Matrix
- #-@ — Vector
- #/ — Matrix
- #/ — Vector
- #== — Matrix
- #== — Vector
- #[] — Matrix
- #[] — Vector
- #[]= — Matrix
- #[]= — Vector
- #abs — Matrix
- #adjoint — Matrix
- #adjugate — Matrix
- #angle_with — Vector
- #antisymmetric? — Matrix
- #build_eigenvectors — Matrix::EigenvalueDecomposition
- #cdiv — Matrix::EigenvalueDecomposition
- #check_int — Matrix
- #check_range — Matrix
- #coerce — Matrix
- #coerce — Vector
- #cofactor — Matrix
- #cofactor_expansion — Matrix
- #collect — Matrix
- #collect — Vector
- #collect! — Matrix
- #collect! — Vector
- #collect2 — Vector
- #column — Matrix
- #column_vectors — Matrix
- #combine — Matrix
- #component — Matrix
- #component — Vector
- #conj — Matrix
- #conjugate — Matrix
- #covector — Vector
- #cross — Vector
- #cross_product — Vector
- #d — Matrix::EigenvalueDecomposition
- #det — Matrix
- #det — Matrix::LUPDecomposition
- #det_e — Matrix
- #determinant — Matrix
- #determinant — Matrix::LUPDecomposition
- #determinant_bareiss — Matrix
- #determinant_e — Matrix
- #diagonal? — Matrix
- #diagonalize — Matrix::EigenvalueDecomposition
- #dot — Vector
- #each — Matrix
- #each — Vector
- #each2 — Vector
- #each_with_index — Matrix
- #eigen — Matrix
- #eigensystem — Matrix
- #eigenvalue_matrix — Matrix::EigenvalueDecomposition
- #eigenvalues — Matrix::EigenvalueDecomposition
- #eigenvector_matrix — Matrix::EigenvalueDecomposition
- #eigenvector_matrix_inv — Matrix::EigenvalueDecomposition
- #eigenvectors — Matrix::EigenvalueDecomposition
- #element — Matrix
- #element — Vector
- #elements_to_f — Matrix
- #elements_to_f — Vector
- #elements_to_i — Matrix
- #elements_to_i — Vector
- #elements_to_r — Matrix
- #elements_to_r — Vector
- #empty? — Matrix
- #entrywise_product — Matrix
- #eql? — Matrix
- #eql? — Vector
- #find_index — Matrix
- #first_minor — Matrix
- #freeze — Matrix
- #freeze — Vector
- #hadamard_product — Matrix
- #hash — Matrix
- #hash — Vector
- #hermitian? — Matrix
- #hessenberg_to_real_schur — Matrix::EigenvalueDecomposition
- #hstack — Matrix
- #imag — Matrix
- #imaginary — Matrix
- #independent? — Vector
- #index — Matrix
- #initialize_copy — Matrix
- #initialize_copy — Vector
- #inner_product — Vector
- #inspect — Matrix
- #inspect — Vector
- #inv — Matrix
- #inverse — Matrix
- #l — Matrix::LUPDecomposition
- #laplace_expansion — Matrix
- #lower_triangular? — Matrix
- #lup — Matrix
- #lup_decomposition — Matrix
- #magnitude — Vector
- #map — Matrix
- #map — Vector
- #map! — Matrix
- #map! — Vector
- #map2 — Vector
- #minor — Matrix
- #norm — Vector
- #normal? — Matrix
- #normalize — Vector
- #orthogonal? — Matrix
- #p — Matrix::LUPDecomposition
- #permutation? — Matrix
- #power_int — Matrix
- #r — Vector
- #rank — Matrix
- #rank_e — Matrix
- #real — Matrix
- #real? — Matrix
- #rect — Matrix
- #rectangular — Matrix
- #reduce_to_hessenberg — Matrix::EigenvalueDecomposition
- #regular? — Matrix
- #rotate_entries — Matrix
- #round — Matrix
- #round — Vector
- #row — Matrix
- #row_count — Matrix
- #row_size — Matrix
- #row_vectors — Matrix
- #set_col_range — Matrix
- #set_column_vector — Matrix
- #set_component — Matrix
- #set_component — Vector
- #set_element — Matrix
- #set_element — Vector
- #set_range — Vector
- #set_row_and_col_range — Matrix
- #set_row_range — Matrix
- #set_value — Matrix
- #set_value — Vector
- #singular? — Matrix
- #singular? — Matrix::LUPDecomposition
- #size — Vector
- #skew_symmetric? — Matrix
- #solve — Matrix::LUPDecomposition
- #square? — Matrix
- #symmetric? — Matrix
- #t — Matrix
- #to_a — Matrix
- #to_a — Vector
- #to_a — Matrix::EigenvalueDecomposition
- #to_a — Matrix::LUPDecomposition
- #to_ary — Matrix::EigenvalueDecomposition
- #to_ary — Matrix::LUPDecomposition
- #to_matrix — Matrix
- #to_matrix — Vector
- #to_s — Matrix
- #to_s — Vector
- #tr — Matrix
- #trace — Matrix
- #transpose — Matrix
- #tridiagonalize — Matrix::EigenvalueDecomposition
- #u — Matrix::LUPDecomposition
- #unitary? — Matrix
- #upper_triangular? — Matrix
- #v — Matrix::EigenvalueDecomposition
- #v_inv — Matrix::EigenvalueDecomposition
- #vstack — Matrix
- #zero? — Matrix
- #zero? — Vector