๐Ÿงฎ Matrix & Vectors

Linear algebra operations on matrices and vectors. Matrices use nested list syntax: {{1,2},{3,4}}.

โœ“ 10 Implemented โณ 2 Coming Soon
Matrix Operations โ€” Implemented
Determinante( <Matrix> )
Aliases: det, Det, determinant
โœ“ Done
Determinant of a square matrix. Negative means the matrix flips orientation.
Determinante({{1,2},{3,4}})         โ†’ -2
Determinante({{1,0,0},{0,2,0},{0,0,3}})  โ†’ 6
Invertiere( <Matrix> )
Aliases: invert, Invert, Inverse, MatrixInverse
โœ“ Done
Inverse of a matrix (exists only when determinant โ‰  0). A ร— Aโปยน = Identity.
Invertiere({{1,2},{3,4}})   โ†’ {{-2,1},{1.5,-0.5}}
Transponiere( <Matrix> )
Aliases: transpose, Transpose
โœ“ Done
Transpose โ€” rows become columns, columns become rows.
Transponiere({{1,2,3},{4,5,6}})   โ†’ {{1,4},{2,5},{3,6}}
Rang( <Matrix> )
Aliases: rank, Rank, MatrixRank
โœ“ Done
Rank of a matrix โ€” number of linearly independent rows (or columns).
Rang({{2,2},{1,1}})     โ†’ 1  (linearly dependent rows)
Rang({{1,2},{3,4}})     โ†’ 2  (full rank)
Treppennormalform( <Matrix> )
Aliases: rref, RREF, ReducedRowEchelon
โœ“ Done
Reduced Row Echelon Form. Use for solving systems of linear equations.
Treppennormalform({{1,2,3},{4,5,6},{7,8,10}})
โ†’ {{1,0,0},{0,1,0},{0,0,1}}
Einheitsmatrix( <n> )
Aliases: identity, IdentityMatrix
โœ“ Done
Returns the nร—n identity matrix (1s on diagonal, 0s elsewhere).
Einheitsmatrix(3)
โ†’ {{1,0,0},{0,1,0},{0,0,1}}
Dimension( <Matrix> )
Aliases: dim, Dim
โœ“ Done
Returns {rows, columns} for a matrix, or element count for a vector.
Dimension({{1,2,3},{4,5,6}})   โ†’ 2 ร— 3
Dimension({1, 2, 3, 4, 5})    โ†’ 5
MatrixAnwenden( <Matrix>, <Objekt> )
Aliases: matapply, ApplyMatrix
โœ“ Done
Applies a matrix transformation to a point or vector. 2ร—2 for 2D, 3ร—3 for 3D.
MatrixAnwenden({{0,-1},{1,0}}, {3,4})   โ†’ (-4, 3)  (90ยฐ rotation)
Vector Operations โ€” Implemented
Skalarprodukt( <u>, <v> )
Aliases: dot, DotProduct (also: Skalarprodukt in Algebra section)
โœ“ Done
Dot product uยทv = ฮฃ(uแตขยทvแตข). Returns a scalar.
Skalarprodukt({1,3,2}, {0,3,-2})   โ†’ 5
Kreuzprodukt( <u>, <v> )
Aliases: cross, CrossProduct
โœ“ Done
Cross product uร—v. For 3D vectors returns a perpendicular vector; for 2D returns the z-component scalar.
Kreuzprodukt({1,3,2}, {0,3,-2})   โ†’ (-12, 2, 3)
Kreuzprodukt({1,2}, {4,5})        โ†’ -3
Coming Soon
Einheitsnormalvektor( <Vektor> )
โณ Soon
Unit normal vector perpendicular to the given vector (rotated 90ยฐ, normalized to length 1).
Einheitsnormalvektor((3, 4))   โ†’ (-0.8, 0.6)
Vektor( <Punkt> ) / Vektor( <A>, <B> )
โณ Soon
Create position vector from origin to a point, or direction vector from A to B.
Vektor((3, 2))          โ†’ vector (3, 2)
Vektor((1,1), (3,4))    โ†’ vector (2, 3)

๐Ÿ’ก Matrix Input Format

Matrices are entered as nested lists. Rows separated by commas inside inner braces:

-- 2ร—2 Matrix
A = {{1, 2}, {3, 4}}

-- 3ร—3 Matrix
B = {{1,0,0}, {0,1,0}, {0,0,1}}

-- Operations
Determinante(A)       โ†’ -2
Invertiere(A)         โ†’ inverse
Transponiere(A)       โ†’ transposed
Treppennormalform(A)  โ†’ RREF