Matrix Operations vs Thermonator Thermodynamics

Matrix Operations Calculator solves every operation step by step — and lets you pick the method. From a quick determinant to a full singular value decomposition, you get the complete worked solution, not just the answer. Works fully offline. SYSTEMS OF LINEAR EQUATIONS CALCULATOR * Gaussian elimination * Cramer's rule * Gauss-Jordan * Inverse matrix method * Montante (Bareiss algorithm) DETERMINANT CALCULATOR * Decomposition * Reduction to triangular form * Montante (Bareiss algorithm) * Sarrus' rule (3×3 only) INVERSE MATRIX CALCULATOR * Gaussian elimination * Gauss-Jordan * Algebraic complements * Montante (Bareiss algorithm) RANK OF A MATRIX CALCULATOR * Elementary transformations * Bordering minors QR DECOMPOSITION CALCULATOR * Gram–Schmidt * Householder reflections * Givens rotation MORE OPERATIONS * Polar decomposition calculator * Matrix square root calculator * Singular value decomposition (SVD) calculator * Eigenvalues, eigenvectors & eigendecomposition (diagonalization) calculator * Matrix minor, cofactor & adjoint calculator * LU, Schur & Cholesky decomposition calculator * Solving matrix equations calculator * Raising a matrix to a power calculator * Multiplying a matrix by a number calculator * Transposition, addition, subtraction & multiplication calculator FEATURES * Step-by-step solutions for every operation * Custom keyboard for fast data entry * Save and edit your solutions * Works without an internet connection * Results as ordinary or decimal fractions Web version: https://matrix-operations.com

- Thermodynamic calculator to solve problems and exercises from Thermodynamic Engineering books. - Quickly calculates steam tables for water, air, ideal gases, refrigerants and other substances. - Contains help and explanations of the main theoretical concepts, equations, first and second thermodynamic laws, etc. FUNCTIONALITIES No advertising. Interactive graph. Share results. Educational aids - Step-by-step calculations. - Solved exercises. - Quick reminders on thermodynamic concepts and formulas. Settings - Control system: Control mass, Control volume. - Sign convention: ΔU = Q − W, ΔU = Q + W. - Reference state: Normal boiling point, ASHRAE, IIR, Çengel-Boles, Moran-Shapiro, Reynolds, Sonntag-Van Wylen-Borgnakke. - Dead state: EPA, ISO, IUPAC, NIST. - Units: International System of Units, Imperial System of Units, Traditional US units. Calculations - Properties: State, Saturation, Process, Cycle. - Calculation of states, processes, and cycles. - Warnings for sensitive calculations: Critical point, Saturation dome (PT), Liquid (v), Gas (Th). - Processes: Polytropic, Isobar, Isotherm, Isochore, Isenthalpic, Adiabatic. - Substances: Water, Noble gases, Ideal gases, Ideal gases (cp Variable), Custom gas. Calculation wizards - Units converter: Pressure, Temperature, Volume, Mass, Energy, Power. - Interpolation: One dimension, Two dimensions. - Mass: Calculate the properties that depend on the mass. - Saturation: Calculate the states of saturated liquid and saturated vapor. Results reports - Substances: Formula, Molecular mass, Critical point, Normal boiling point, Specific heat. - Summary: Settings, States, Processes, Cycles. - Calculations: Step-by-step calculations. - Balances: Mass balance. PREMIUM Calculations - Processes: Irreversible, Inlet+Exit, Branches, Reheating, Subcooling. - Substances: Real substances (Acetone, Air, Ammonia, Benzene, Butane, Carbon dioxide, Ethane, Ethanol, Ethylene, Heptane, Hexane, Isobutane, Isopentane, Methane, Nitrogen, Octane, Oxygen, Pentane, Propane, Propanol, Propylene, R-11, R-114, R-12, R-123, R-1234yf, R-124, R-13, R-134a, R-14, R-22, R-23, R-32, R-404a, R-407c, R-410a, R-500, R-502, R-507a, R-C318, SES36, Water). Calculation wizards - Energy balance: Solve exercises of Unknown process, Internal friction, Kinetic energy, Potential energy, etc. - Entropy balance: Solve exercises of Internal generated entropy, External generated entropy, Universe entropy increment, Destroyed exergy, etc. - Heat exchangers: Generic, Closed, Open, Mixed. - Cycles: Automatically solve 24 types of cycles. Basic cycles (1 Cycle), Combustion engines (4 Cycles), Gas turbine (5 Cycles), Steam turbine (2 Cycles), Steam turbine with regenerative preheating (4 Cycles), Vapor-compression refrigeration (6 Cycles), Gas refrigeration (2 Cycles). Results reports - Balances: Energy balance, Boundary work, Entropy balance, Internal generated entropy, External generated entropy, Universe entropy increment, Destroyed exergy (Irreversibility). Exercises - Open and save exercises. Terms of use (EULA) https://www.apple.com/legal/internet-services/itunes/dev/stdeula