Enhance Your Learning with Matrices and Determinants Flash Cards for quick learning
A rectangular array of numbers, symbols, or expressions arranged in rows and columns.
A horizontal line of elements in a matrix.
A vertical line of elements in a matrix.
A matrix with an equal number of rows and columns.
A square matrix with ones on the main diagonal and zeros elsewhere.
A matrix obtained by interchanging its rows with columns.
The operation of combining two matrices by adding corresponding elements.
The operation of multiplying a matrix by a scalar (a single number).
The operation of combining two matrices by multiplying corresponding elements and summing the products.
A scalar value associated with a square matrix, used to determine properties and solutions.
A scalar value associated with a specific element of a matrix, used in the calculation of determinants.
A determinant obtained by deleting the row and column containing a specific element of a matrix.
A matrix obtained by taking the transpose of the matrix of cofactors.
A matrix that, when multiplied by the original matrix, gives the identity matrix.
A method for solving a system of linear equations using determinants.
A scalar value that represents a factor by which a matrix stretches or compresses a vector.
A non-zero vector that, when multiplied by a matrix, results in a scalar multiple of itself.
A matrix that can be expressed as a product of three matrices: P, D, and P^-1, where D is a diagonal matrix.
A square matrix that is equal to its transpose.
A square matrix that is equal to the negation of its transpose.
A square matrix whose transpose is equal to its inverse.
The process of expressing a matrix as a product of eigenvectors and eigenvalues.
The process of expressing a matrix as a product of three matrices: U, Σ, and V^T, where U and V are orthogonal matrices and Σ is a diagonal matrix.
The maximum number of linearly independent rows or columns in a matrix.
The set of all vectors that, when multiplied by a matrix, result in the zero vector.
The set of all linear combinations of the rows of a matrix.
The set of all linear combinations of the columns of a matrix.
The set of all vectors that are orthogonal to a given subspace.
A matrix that projects vectors onto a subspace.
A method for finding the best-fit solution to an overdetermined system of equations.
A symmetric matrix that has positive eigenvalues.
A symmetric matrix that has non-negative eigenvalues.
A symmetric matrix that has negative eigenvalues.
A symmetric matrix that has non-positive eigenvalues.
A square matrix that is equal to its conjugate transpose.
A square matrix whose conjugate transpose is equal to its inverse.
The process of expressing a Hermitian matrix as a product of eigenvectors and eigenvalues.
A square matrix that does not have an inverse.
The product of the main diagonal elements minus the product of the off-diagonal elements.
The sum of the products of each element with its cofactor.
The sum of the products of each element with its cofactor.
The product of the diagonal elements.
The product of the diagonal elements.
The product of the diagonal elements.
The product of the determinants of the diagonal blocks.
The determinant of a matrix is equal to the determinant of its transpose.
The product of the determinants of two matrices is equal to the determinant of their product.
The determinant of a matrix is equal to the reciprocal of the determinant of its inverse.
The determinant of a scalar multiple of a matrix is equal to the scalar raised to the power of the matrix's dimension multiplied by the determinant of the original matrix.
The determinant of the sum of two matrices is equal to the sum of their determinants.
The determinant of the difference of two matrices is equal to the difference of their determinants.
The determinant of a matrix raised to a power is equal to the determinant of the matrix raised to that power.
The determinant of a zero matrix is equal to zero.
The determinant of an identity matrix is equal to one.
The determinant of a block matrix is equal to the product of the determinants of its diagonal blocks.
The determinant of a triangular matrix is equal to the product of its diagonal elements.
The determinant of a skew-symmetric matrix is equal to zero.
The determinant of a symmetric matrix is equal to the product of its eigenvalues.
The determinant of a Hermitian matrix is equal to the product of its eigenvalues.
The determinant of a unitary matrix is equal to the product of its eigenvalues, which have unit modulus.
The determinant of a positive definite matrix is positive.
The determinant of a positive semidefinite matrix is non-negative.
The determinant of a negative definite matrix is negative.
The determinant of a negative semidefinite matrix is non-positive.
The determinant of a singular matrix is equal to zero.