Linear Algebra Decoded
Price: $29.00
Version: 1.50
Operating System: Windows
Size: 3.15 MB (3234 KB)
List of problems that can be solved using Linear Algebra Decoded
Click on links to see examples to problems solved by Linear Algebra Decoded
Matrices, determinants and linear equations |
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| Compute the sum of two matrices. |
| Compute the difference of two matrices. |
| Compute the product of a matrix by a scalar. |
| Compute the product of two matrices. |
| Compute the product of a square matrix by itself. |
| Find the transpose of a matrix. |
| Calculate the determinant of a square matrix. |
| Transform a matrix to row echelon form using elementary row transformations. |
| Calculate the rank of a matrix, transforming it first to row echelon form. |
| Compute the matrix of cofactors. |
| Compute the adjugate matrix. |
| Compute the inverse of a matrix using the adjugate matrix. |
| Compute the inverse of a matrix using row operations. |
| Find the LU factorization for a matrix. |
| Classify a system of linear equations. |
| Solve a system of linear equations using Gaussian elimination. |
Vector spaces and subspaces |
| Express a vector as a linear combination of a set of vectors. |
| Determine if a set of vectors from a vector space is linearly dependent or independent. |
| Find the vector subspace spanned by a set of vectors. |
| Calculate the dimension of a vector subspace expressed by its implicit equations. |
| Extract a basis from a spanning set. |
| Find a basis for a vector subspace expressed by its implicit equations. |
| Determine if a set of vectors is a basis for a subspace expressed by its implicit equations. |
| Determine if a set of vectors is a basis for the subspace spanned by another set of vectors. |
| Expand a set of vectors into a basis for the vector space. |
| Find the coordinate vector of a given vector, relative to a basis for the vector space. |
| Determine which vectors of a basis for the vector space can be replaced for a given vector, in order that the new set of vectors continues being a basis for the vector space. |
| Compute the change of basis matrix. |
| Find the subspace obtained from the intersection of two subspaces which are expressed by their implicit equations. |
| Find the subspace obtained from the intersection of two subspaces which are given by spanning sets. |
| Find the subspace obtained from the intersection of two subspaces, where the first one is expressed by its implicit equations, and the second one by a spanning set. |
| Find the subspace obtained from the sum of two subspaces which are expressed by their implicit equations. |
| Find the subspace obtained from the sum of two subspaces which are given by spanning sets. |
| Find the subspace obtained from the sum of two subspaces, where the first one is expressed by its implicit equations, and the second one by a spanning set. |
| Determine if two subspaces which are expressed by their implicit equations, are complementary subspaces. |
| Determine if two subspaces which are given by spanning sets, are complementary subspaces. |
| Determine if two subspaces are complementary subspaces, where the first one is expressed by its implicit equations, and the second one by a spanning set. |
| Find a complementary subspace for a given subspace expressed by its implicit equations. |
| Find a complementary subspace for the subspace spanned by a set of vectors. |
| Determine if two subspaces which are expressed by their implicit equations, are equal. |
| Determine if two subspaces which are given by spanning sets, are equal. |
| Determine if two subspaces are equal, where the first one is expressed by its implicit equations, and the second one by a spanning set. |
Linear transformations |
| Find the matrix of a linear transformation with respect to the standard bases. |
| Find the matrix of a linear transformation with respect to two given bases, one for the input space and the other one for the output space. |
| Compute the image of a given vector under a linear transformation. |
| Find a basis and the parametric representation of the kernel (null-space) of a linear transformation. |
| Find a basis and the implicit equations of the image (range) of a linear transformation. |
| Determine if the kernel and the image of an endomorphism are complementary subspaces. |
| Classify a linear transformation. |
| Find a linear transformation that maps an ordered set of vectors of the input space in an ordered set of vectors of the output space. |
| Find a linear transformation which image can be spanned by a given set of vectors. |
| Find the linear transformation resulting from adding two linear transformations. |
| Find the linear transformation resulting from multiplying a linear transformation by a scalar. |
| Find the linear transformation resulting from composing two linear transformations. |
| Find the inverse of a linear transformation. |
| Find the characteristic polynomial associated to a linear transformation. |
| Find the eigenvalues and eigenvectors of a linear transformation. |
| Determine if a linear transformation is diagonalizable. |
| Determine if a subspace expressed by its implicit equations, is invariant with respect to a linear transformation. |
| Determine if the subspace spanned by a set of vectors is invariant with respect to a linear transformation. |