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10. 行列(標準数学函数)


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10.0.1 matrix_clone

matrix_clone(M)

: It generates the clone of the matrix M.

Example:

 
 matrix_clone(matrix_list_to_matrix([[1,1],[0,1]]));

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10.0.2 matrix_det

matrix_det(M)

: It returns the determinant of the matrix M.

Example:

 
 poly_factor(matrix_det([[1,x,x^2],[1,y,y^2],[1,z,z^2]]));

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10.0.3 matrix_diagonal_matrix

matrix_diagonal_matrix(L)

: It returns the diagonal matrix with diagonal entries L.

Example:

 
 matrix_diagonal_matrix([1,2,3]);

References:

matrix_list_to_matrix


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10.0.4 matrix_eigenavalues

matrix_eigenavalues(M)

: It returns the eigenvalues of the matrix M.

Example:

 
 matrix_eigenvalues([[x,1],[0,y]]);

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10.0.5 matrix_identity_matrix

matrix_identity_matrix(N)

: It returns the identity matrix of the size N.

Example:

 
 matrix_identity_matrix(5);

References:

matrix_diagonal_matrix


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10.0.6 matrix_image

matrix_image(M)

: It computes the image of M. Redundant vectors are removed.

Example:

 
 matrix_image([[1,2,3],[2,4,6],[1,0,0]]);

References:

matrix_kernel


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10.0.7 matrix_inner_product

matrix_inner_product(A,B)

: It returns the inner product of two vectors A and B.

Example:

 
 matrix_inner_product([1,2],[x,y]);

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10.0.8 matrix_inverse

matrix_inverse(M)

: It returns the inverse of the matrix M.

Example:

 
 matrix_inverse([[1,2],[0,1]]);

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10.0.9 matrix_kernel

matrix_kernel(M)

: It returns the basis of the kernel of the matrix M.

Example:

 
 matrix_kernel([[1,1,1,1],[0,1,3,4]]);

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10.0.10 matrix_list_to_matrix

matrix_list_to_matrix(M)

: It translates the list M to a matrix.

Example:

 
 print_xdvi_form(matrix_list_to_matrix([[1,1],[0,2]]));

References:

matrix_matrix_to_list


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10.0.11 matrix_matrix_to_list

matrix_matrix_to_list(M)

: It translates the matrix M to a list.

References:

matrix_list_to_matrix


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10.0.12 matrix_rank

matrix_rank(M)

: It returns the rank of the matrix M.

Example:

 
 matrix_rank([[1,1,1,1],[0,1,3,4]]);

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10.0.13 matrix_solve_linear

matrix_solve_linear(M,X,B)

: It solves the system of linear equations M X = B

Example:

 
 matrix_solve_linear([[1,2],[0,1]],[x,y],[1,2]);

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10.0.14 matrix_submatrix

matrix_submatrix(M,Ind)

: It returns the submatrix of M defined by the index set Ind.

Example:

 
 matrix_submatrix([[0,1],[2,3],[4,5]],[1,2]);

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10.0.15 matrix_transpose

matrix_transpose(M)

: It returns the transpose of the matrix M.

References:

matrix_list_to_matrix


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