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The 24 pages that link to Linear combination, each with the reason it gives.

• Vector spaceRelated: Linear combinations are the basic expressions formed from vectors and scalars.

• Linear algebraRelated: Linear combinations define span, dependence, and many solutions to linear systems.

• Basis (linear algebra)Related: Spanning and unique representation are both expressed through linear combinations.

• Quantum superpositionRelated: Superposition uses this mathematical structure, with quantum amplitudes as coefficients.

• Gaussian eliminationRelated: Row replacement combines equations using scalar multiples.

• VectorRelated: Every vector in a span is built from selected vectors by this operation.

• Linear independenceNarrower topic: Independence asks whether a linear combination can vanish with any nonzero coefficient.

• Principal component analysisNarrower topic: Each principal component is a weighted linear combination of the original variables.

• Distributive propertyRelated: Scalar multiplication distributes over vector addition in linear combinations.

• Linear mapRelated: Preserving addition and scalar multiplication means preserving every linear combination.

• System of linear equationsRelated: A system asks whether its constants vector is a combination of coefficient columns.

• Quotient spaceRelated: Linear combinations of cosets define addition and scalar multiplication in V/W.

• Affine combinationNarrower topic: An affine combination is a linear combination with the additional requirement that its coefficients sum to one.

• Convex combinationCompared with: Unlike a convex combination, its coefficients need not be nonnegative or sum to one.

• Lindemann–Weierstrass theoremRelated: The theorem forbids a nonzero algebraic-coefficient linear combination of the exponential values from vanishing.

• Scalar multiplicationRelated: It combines scalar multiplication with vector addition.

• Bézout's identityNarrower topic: The identity characterizes the gcd as a linear combination of its two inputs.

• Finite-dimensional vector spaceRelated: A basis spans the space when every vector is a linear combination of its vectors.

• Vector geometryRelated: It expresses points and directions using selected vectors as building blocks.

• Column spaceNarrower topic: Every vector in a column space is formed by combining columns this way.

• Linear combination of atomic orbitalsNarrower topic: LCAO applies this mathematical operation to atomic-orbital wavefunctions.

• Euclidean vectorRelated: Vector addition and scalar multiplication combine Euclidean vectors into new vectors.

• Cone (convex analysis)Related: Convex cones contain nonnegative linear combinations of their vectors.

• Steinitz exchange lemmaRelated: The exchange step expresses a chosen independent vector using the current spanning set.