Matrix Online Calculators
Professional online calculators for 3×3 and 4×4 matrix operations
3×3 Matrix Operations
Arithmetic Operations
Addition 3×3
Add two 3×3 matrices element by element
Subtraction 3×3
Subtract one 3×3 matrix from another
Multiplication 3×3
Multiply two 3×3 matrices (Matrix × Matrix)
Scalar Multiplication 3×3
Multiply a 3×3 matrix by a scalar value
Rotation Operations
X-Axis Rotation 3×3
Rotation matrix around the X-axis (Roll)
Y-Axis Rotation 3×3
Rotation matrix around the Y-axis (Pitch)
Z-Axis Rotation 3×3
Rotation matrix around the Z-axis (Yaw)
Yaw-Pitch-Roll Rotation 3×3
Combined XYZ rotation, quaternion conversion
Euler Angles to Matrix 3×3
Convert Euler angles to a rotation matrix
Matrix to Euler Angles 3×3
Extract Euler angles from rotation matrix
Advanced Operations
Invert Matrix 3×3
Calculate the inverse of a 3×3 matrix
Determinant 3×3
Calculate the determinant of a 3×3 matrix
4×4 Matrix Operations
Arithmetic Operations
Addition 4×4
Add two 4×4 matrices element by element
Subtraction 4×4
Subtract one 4×4 matrix from another
Multiplication 4×4
Multiply two 4×4 matrices (Matrix × Matrix)
Scalar Multiplication 4×4
Multiply a 4×4 matrix by a scalar value
Rotation Operations
X-Axis Rotation 4×4
Homogeneous rotation around X-axis
Y-Axis Rotation 4×4
Homogeneous rotation around Y-axis
Z-Axis Rotation 4×4
Homogeneous rotation around Z-axis
Yaw-Pitch-Roll Rotation 4×4
Combined XYZ rotation with homogeneous coordinates
Vector Rotation 4×4
Rotate a vector using a 4×4 rotation matrix
Advanced Operations
Invert Matrix 4×4
Calculate the inverse of a 4×4 matrix
Determinant 4×4
Calculate the determinant of a 4×4 matrix
Matrix Interpolation 4×4
Interpolate between two 4×4 matrices
About Matrix Calculators
These matrix calculators are essential tools for linear algebra, computer graphics, and engineering. They help in understanding and calculating:
- Matrix Operations - Add, subtract, multiply
- 3D Rotations - X, Y, Z axis rotations
- Euler Angles - Yaw, pitch, roll
- Transformations - 3D graphics, robotics
- Matrix Properties - Determinant, inverse
- Homogeneous Coords - 4×4 transformations
Key Applications
3×3 Matrices
• Linear transformations
• 3D rotation matrices
• Systems of equations
• 3D rotation matrices
• Systems of equations
4×4 Matrices
• Homogeneous coordinates
• 3D graphics transformations
• Translation + rotation combined
• 3D graphics transformations
• Translation + rotation combined
Rotation Matrices
• Single-axis rotations (X, Y, Z)
• Euler angles (yaw-pitch-roll)
• Quaternion conversions
• Euler angles (yaw-pitch-roll)
• Quaternion conversions
Matrix Arithmetic
• Element-wise operations
• Matrix multiplication
• Scalar multiplication
• Matrix multiplication
• Scalar multiplication
Tip: 4×4 matrices with homogeneous coordinates are the standard
in computer graphics, allowing translation, rotation, and scaling to be combined
in a single transformation.
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Quick Reference
A + B
Addition
A × B
Multiplication
A-1
Inverse
det(A)
Determinant
Rx,y,z(θ)
Rotation
Matrix Dimensions
3×3 Matrices
9 elements, rotation only
9 elements, rotation only
4×4 Matrices
16 elements, rotation + translation
16 elements, rotation + translation