Basis
A basis is a linearly independent set of vectors that spans a vector space.
Definition · Example · CSE Use →Linear Algebra
Definitions, examples and Computer Science applications for this mathematics subject.
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Determinant
The determinant is a scalar associated with a square matrix that indicates properties such as invertibility and area scaling.
Definition · Example · CSE Use →Dot Product
The dot product multiplies corresponding vector components and adds the results.
Definition · Example · CSE Use →Eigenvalue
An eigenvalue is a scalar λ for which a non-zero vector v satisfies Av=λv.
Definition · Example · CSE Use →Eigenvector
An eigenvector is a non-zero vector whose direction is unchanged by a linear transformation, except for scaling.
Definition · Example · CSE Use →Identity Matrix
An identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere.
Definition · Example · CSE Use →Inverse Matrix
The inverse of a square matrix A is a matrix A⁻¹ such that their product is the identity matrix.
Definition · Example · CSE Use →Linear Independence
Vectors are linearly independent when no non-trivial linear combination of them equals the zero vector.
Definition · Example · CSE Use →Matrix
A matrix is a rectangular array of numbers arranged in rows and columns.
Definition · Example · CSE Use →Matrix Multiplication
Matrix multiplication combines rows of the first matrix with columns of the second.
Definition · Example · CSE Use →Rank
The rank of a matrix is the dimension of its row space or column space and measures the number of independent directions.
Definition · Example · CSE Use →Scalar
A scalar is a single numerical value used to scale quantities such as vectors or matrices.
Definition · Example · CSE Use →Transpose
The transpose of a matrix swaps its rows and columns.
Definition · Example · CSE Use →Vector
A vector is an ordered list of numbers that can represent magnitude and direction or a point in feature space.
Definition · Example · CSE Use →Vector Magnitude
Vector magnitude is the length or norm of a vector.
Definition · Example · CSE Use →