Vector projection

Definition

The vector projection of a vector a on a non-zero vector b is the orthogonal projection of a onto a straight line parallel to b. The projection of a onto b is often written as or a∥b.

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(0,1)-matrix Adjugate matrix Affine coordinate system Affine geometry Affine group Affine space Affine transformation Angle Antihermitian matrix Basic Linear Algebra Subprograms Basis (linear algebra)Basis transformation matrix Bivector Block matrix Cartesian coordinate system Category of vector spaces Cauchy–Binet formula Cayley–Hamilton theorem Change of basis Characteristic polynomial Cholesky decomposition Circulant matrix Classical treatment of tensors Clifford algebra Comparison of linear algebra libraries Component-free treatment of tensors Cramer's rule Cyclic subspace Determinant Diagonal matrix Dimension theorem for vector spaces Dot product Dual space Eigenvalue, eigenvector and eigenspace Elementary row operations Euclidean group Euclidean norm Euclidean space Examples of vector spaces Exterior algebra Flat (geometry)Floating-point arithmetic Galilean group Gamas's theorem Gaussian elimination Gauss–Jordan elimination Geometric algebra Glossary of linear algebra Gram–Schmidt process Hamel basis Hamel dimension Hankel matrix Haynsworth inertia additivity formula Hermitian matrix Hessenberg matrix Hessian matrix Higher-order singular value decomposition Householder transformation Hyperplane Improper rotation Indefinite orthogonal group Inner product space Jordan normal form LU decomposition Least squares Length Linear algebra Linear combination Linear equation Linear functional Linear independence Linear least squares Linear map Linear span Linear subspace List of matrices Matrix (mathematics)Matrix addition Matrix congruence Matrix consimilarity Matrix decomposition Matrix equivalence Matrix inversion Matrix multiplication Matrix similarity Minor (linear algebra)Moore–Penrose pseudoinverse Multilinear algebra Multivector Normed vector space Null space Null vector Nullity theorem Numerical linear algebra Numerical stability Opposite vector Orientation (geometry)Orthogonal Orthogonal complement Orthogonal group Orthogonal matrix Orthogonal projection Orthogonality Orthonormality Outer product Outline of linear algebra Overcompleteness Perpendicular Perron–Frobenius theorem Pfaffian Plane (geometry)Poincaré group Polar decomposition Positive-definite matrix Projection (linear algebra)Projection (mathematics)Projective geometry Projective linear group Projective space Projective transformation Pseudo-Euclidean space QR decomposition Quadric Rank (linear algebra)Rank–nullity theorem Reducing subspace Right angle Row and column spaces Row equivalence Scalar projection Scale factor Schur complement Schur decomposition Separating axis theorem Shear mapping Singular value decomposition Skew-symmetric matrix Sparse matrix Spectral theorem Spectrum of a matrix Squeeze mapping Stochastic matrix Straight angle Straight line Strassen algorithm Symmetric algebra Symmetric matrix Symplectic structure System of linear equations Tensor Tensor algebra Toeplitz matrix Topological vector space Trace (linear algebra)Transpose Triangular matrix Tridiagonal matrix Unit vector Unitary matrix Vandermonde matrix Vector (geometry)Vector notation Vector space Weyr canonical form Woodbury matrix identity Zero vector

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