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Linear Algebra Decoded
 

Linear Algebra Decoded

Linear Algebra Decoded
Version: 1.26
Price: $22.95 USD  (Full version - Buy Now)
Downloadable version: Demo version - Limited functionalities
Operating system: Windows XP / Vista / 7 / 8
Size: 3.2 MB (3270 KB)
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List of problems that can be solved using Linear Algebra Decoded

The examples are solutions to problems solved by Linear Algebra Decoded
topicMatrices, determinants and linear equations
bulletCompute the sum of two matrices.View example
bulletCompute the difference of two matrices.
bulletCompute the product of a matrix by a scalar.
bulletCompute the product of two matrices.View example
bulletCompute the product of a square matrix by itself.
bulletFind the transpose of a matrix.
bulletCalculate the determinant of a square matrix.View example
bulletTransform a matrix to row echelon form using elementary row transformations.View example
bulletCalculate the rank of a matrix, transforming it first to row echelon form.
bulletCompute the matrix of cofactors.
bulletCompute the adjugate matrix.
bulletCompute the inverse of a matrix using the adjugate matrix.
bulletCompute the inverse of a matrix using row operations.View example
bulletFind the LU factorization for a matrix.
bulletClassify a system of linear equations.
bulletSolve a system of linear equations using Gaussian elimination.View example
topicVector spaces and subspaces
bulletExpress a vector as a linear combination of a set of vectors.View example
bulletDetermine if a set of vectors from a vector space is linearly dependent or independent.
bulletFind the vector subspace spanned by a set of vectors.View example
bulletCalculate the dimension of a vector subspace expressed by its implicit equations.
bulletExtract a basis from a spanning set.
bulletFind a basis for a vector subspace expressed by its implicit equations.
bulletDetermine if a set of vectors is a basis for a subspace expressed by its implicit equations.
bulletDetermine if a set of vectors is a basis for the subspace spanned by another set of vectors.
bulletExpand a set of vectors into a basis for the vector space.
bulletFind the coordinate vector of a given vector, relative to a basis for the vector space.
bulletDetermine 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.
bulletCompute the change of basis matrix.View example
bulletFind the subspace obtained from the intersection of two subspaces which are expressed by their implicit equations.
bulletFind the subspace obtained from the intersection of two subspaces which are given by spanning sets.
bulletFind 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.
bulletFind the subspace obtained from the sum of two subspaces which are expressed by their implicit equations.View example
bulletFind the subspace obtained from the sum of two subspaces which are given by spanning sets.
bulletFind 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.
bulletDetermine if two subspaces which are expressed by their implicit equations, are complementary subspaces.
bulletDetermine if two subspaces which are given by spanning sets, are complementary subspaces.
bulletDetermine if two subspaces are complementary subspaces, where the first one is expressed by its implicit equations, and the second one by a spanning set.
bulletFind a complementary subspace for a given subspace expressed by its implicit equations.
bulletFind a complementary subspace for the subspace spanned by a set of vectors.
bulletDetermine if two subspaces which are expressed by their implicit equations, are equal.
bulletDetermine if two subspaces which are given by spanning sets, are equal.View example
bulletDetermine if two subspaces are equal, where the first one is expressed by its implicit equations, and the second one by a spanning set.
topicLinear transformations
bulletFind the matrix of a linear transformation with respect to the standard bases.
bulletFind 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.
bulletCompute the image of a given vector under a linear transformation.
bulletFind a basis and the parametric representation of the kernel (null-space) of a linear transformation.View example
bulletFind a basis and the implicit equations of the image (range) of a linear transformation.
bulletDetermine if the kernel and the image of an endomorphism are complementary subspaces.
bulletClassify a linear transformation.
bulletFind a linear transformation that maps an ordered set of vectors of the input space in an ordered set of vectors of the output space.View example
bulletFind a linear transformation which image can be spanned by a given set of vectors.
bulletFind the linear transformation resulting from adding two linear transformations.
bulletFind the linear transformation resulting from multiplying a linear transformation by a scalar.
bulletFind the linear transformation resulting from composing two linear transformations.
bulletFind the inverse of a linear transformation.
bulletFind the characteristic polynomial associated to a linear transformation.
bulletFind the eigenvalues and eigenvectors of a linear transformation.
bulletDetermine if a linear transformation is diagonalizable.View example
bulletDetermine if a subspace expressed by its implicit equations, is invariant with respect to a linear transformation.
bulletDetermine if the subspace spanned by a set of vectors is invariant with respect to a linear transformation.
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