MATH
Matrices, vectors & linear algebra calculators
Calculate vector products, normalize or project a two-dimensional vector, or find the trace, determinant or Frobenius norm of a real 2 by 2 matrix.
Choose the right tool
A dot product is signed and uses corresponding component products. Cross-product magnitude is nonnegative and measures the parallelogram area in squared component units; the tool does not return the cross-product direction. Selected-component tools explicitly choose X or Y; projection needs a nonzero target. Matrix inputs are a,b in the first row and c,d in the second; these specific scalar jobs do not solve general matrices. Matrix transpose, arithmetic, multiplication, cofactor, adjugate and square tools return one explicitly selected row/column entry. Inversion and the two-equation solve use a positive-diagonal skew family with a guaranteed nonzero determinant. Complex-number products, quotients and conjugates return the selected real or imaginary component, with the displayed divisor bounds enforced.
29 tools
- 2 by 2 Matrix Determinant Calculator
2 by 2 Matrix Determinant. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number gives -2 number. Exactly2by2 dimensionless real matrix, row order a,b;c,d; no larger matrix or alternate norm support. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
- 2 by 2 Matrix Frobenius Norm Calculator
2 by 2 Matrix Frobenius Norm. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number gives 5.47722557505 number. Exactly2by2 dimensionless real matrix, row order a,b;c,d; no larger matrix or alternate norm support. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
- 2 by 2 Matrix Trace Calculator
2 by 2 Matrix Trace. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number gives 5 number. Exactly2by2 dimensionless real matrix, row order a,b;c,d; no larger matrix or alternate norm support. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
- 2×2 Adjugate Entry Calculator
2×2 Adjugate Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 4 number. Classical adjugate of real 2×2 matrix; complex Hermitian adjoint deferred. Original useful product scope; historical catalog title does not grant missing modes
- 2×2 Characteristic Polynomial at Lambda Calculator
2×2 Characteristic Polynomial at Lambda Calculator — change the supplied values to calculate 2×2 characteristic polynomial at lambda.
- 2×2 Cofactor Entry Calculator
2×2 Cofactor Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 4 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes o
- 2×2 Hadamard Product Entry Calculator
2×2 Hadamard Product Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, E: 5 number, F: 6 number, G: 7 number, H: 8 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 5 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product sc
- 2×2 Matrix Product Entry Calculator
2×2 Matrix Product Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, E: 5 number, F: 6 number, G: 7 number, H: 8 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 19 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product sco
- 2×2 Matrix Scalar Product Entry Calculator
2×2 Matrix Scalar Product Entry Calculator — change the supplied values to calculate 2×2 matrix scalar product entry.
- 2×2 Matrix Square Entry Calculator
2×2 Matrix Square Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 7 number. Fixed second power only; arbitrary integer powers deferred. Original useful product scope; historical catalog title does not grant missing modes or source
- 2×2 Matrix Sum Entry Calculator
2×2 Matrix Sum Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, E: 5 number, F: 6 number, G: 7 number, H: 8 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 6 number. Addition only, 2×2 real matrices; no subtraction or variable-size matrix claims. Original useful product
- 2×2 Matrix Transpose Entry Calculator
2×2 Matrix Transpose Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 1 number, B: 2 number, C: 3 number, D: 4 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 1 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing
- 2D Cosine Similarity of Two Nonzero Vectors Calculator
2D Cosine Similarity of Two Nonzero Vectors. Example: A x: 3 number, A y: 4 number, B x: 4 number, B y: 3 number gives 0.96 number. Exactly two2D dimensionless Cartesian vectors; both x components≥.1 guarantee nonzero. Numerical score only, not semantic embedding, similarity recommendation or calibrated probability. Only this original stated job is proposed, not full historical source coverage. I
- 2D Linear Combination Component Calculator
2D Linear Combination Component. Coordinate: 0=x, 1=y: x coordinate, y coordinate only. Example: X1: 1 number, Y1: 2 number, X2: 3 number, Y2: 4 number, S: 2 number, T: 3 number, Coordinate: 0=x, 1=y: 0 number gives 11 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parit
- 2D Unit Vector Component with Positive X Component Calculator
2D Unit Vector Component with Positive X Component. Coordinate to return: X coordinate, Y coordinate only. Example: X: 3 units, Y: 4 units, Coordinate to return: 1 selection gives 0.6 number. 2D orthogonal same-unit components, x positive ensures nonzero vector; selected unit component dimensionless. Only this original stated job is proposed, not full historical source coverage. Input domains and
- 2D Vector Difference Component Calculator
2D Vector Difference Component. Coordinate: 0=x, 1=y: x coordinate, y coordinate only. Example: X1: 1 number, Y1: 2 number, X2: 3 number, Y2: 4 number, Coordinate: 0=x, 1=y: 0 number gives -2 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parity.
- 2D Vector Direction with Positive X Component Calculator
2D Vector Direction with Positive X Component. Example: X: 3 units, Y: 4 units gives 53.1301023542 degrees. 2D Cartesian vector, x>0; angle measured counterclockwise from+x, signed -90..90°. No unsupported quadrant claim. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
- 2D Vector Projection Component onto Positive X Direction Vector Calculator
2D Vector Projection Component onto Positive X Direction Vector. Coordinate to return: X coordinate, Y coordinate only. Example: Source x: 3 units, Source y: 4 units, Target x: 1 number, Target y: 2 number, Coordinate to return: 1 selection gives 2.2 units. 2D source components same units; direction target dimensionless and target x≥.1 ensures nonzero; selected component. Only this original stated
- 2D Vector Sum Component Calculator
2D Vector Sum Component. Coordinate: 0=x, 1=y: x coordinate, y coordinate only. Example: X1: 1 number, Y1: 2 number, X2: 3 number, Y2: 4 number, Coordinate: 0=x, 1=y: 0 number gives 4 number. Real bounded inputs with supplied units; numerical selected result only. Original useful product scope; historical catalog title does not grant missing modes or source parity.
- 3D Cross Product Magnitude Calculator
cross product. Example: AX: 2 units, AY: 2 units, AZ: 2 units, BX: 2 units, BY: 2 units, BZ: 2 units gives 0 units². Scalar magnitude only of cross product of two 3D Cartesian vectors. No vector coordinate output or direction promised. Components bounded ±1000 to keep all squared intermediates safe. Elementary arithmetic over the accepted finite domain. No statistical population inference, supplie
- Diagonal 2×2 Largest Eigenvalue Calculator
Diagonal 2×2 Largest Eigenvalue Calculator — change the supplied values to calculate diagonal 2×2 largest eigenvalue.
- Diagonal 2×2 Null Space Dimension Calculator
Diagonal 2×2 Null Space Dimension Calculator — change the supplied values to calculate diagonal 2×2 null space dimension.
- Diagonal 2×2 Rank Calculator
Diagonal 2×2 Rank Calculator — change the supplied values to calculate diagonal 2×2 rank.
- Diagonal 3×3 Largest Singular Value Calculator
Diagonal 3×3 Largest Singular Value Calculator — change the supplied values to calculate diagonal 3×3 largest singular value.
- Dot Product Calculator
dot product. Example: Ax: 2 units, Ay: 2 units, Az: 2 units, Bx: 2 units, By: 2 units, Bz: 2 units gives 12 units². Exactly two 3D Cartesian vectors with matching component units; scalar dot product, no matrix or cross-product inference. Elementary arithmetic over the accepted finite domain. No statistical population inference, supplied-data validity claim or specialist recommendation.
- Euclidean Vector Norm of Three Components Calculator
Euclidean Vector Norm of Three Components. Example: X: 3 units, Y: 4 units, Z: 12 units gives 13 units. Exactly three real orthogonal components in same units; Euclidean norm only. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
- Invertible [[a,b],[-b,d]] Matrix Inverse Entry Calculator
Invertible [[a,b],[-b,d]] Matrix Inverse Entry. Entry: 0=11, 1=12, 2=21, 3=22: Row 1, column 1, Row 1, column 2, Row 2, column 1, Row 2, column 2 only. Example: A: 2 number, B: 1 number, D: 3 number, Entry: 0=11, 1=12, 2=21, 3=22: 0 number gives 0.428571428571 number. Only displayed positive-diagonal skew-offdiagonal 2×2 family; no arbitrary singular-matrix admission. Original useful product scope
- Positive Diagonal 2×2 Spectral Condition Number Calculator
Positive Diagonal 2×2 Spectral Condition Number Calculator — change the supplied values to calculate positive diagonal 2×2 spectral condition number.
- Solve x in a x + b y = p, −b x + d y = q Calculator
Solve x in a x + b y = p, −b x + d y = q. Example: A: 2 number, B: 1 number, D: 3 number, P: 7 number, Q: 4 number gives 2.42857142857 number. Only structured nonsingular real 2×2 system; selected x output, y shown as supporting context. Original useful product scope; historical catalog title does not grant missing modes or source parity.
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