mrdivide — Solve linear systems with right-division in MATLAB and RunMat.

X = A / B (or mrdivide(A, B)) solves X * B = A. Square/nonsingular, rectangular, and rank-deficient solve paths follow MATLAB right-division semantics.

Syntax

X = mrdivide(A, B)

Inputs

Returns

Errors

How mrdivide works

• Scalars divide exactly: A / s scales A by 1/s, while s / B requires B to be scalar.
• Logical and integer inputs are promoted to double precision before solving.
• Purely real operands produce real outputs; any complex operand promotes the computation (and result) to complex arithmetic.
• Inputs must be effectively two-dimensional; trailing singleton dimensions are allowed.
• The number of columns must agree (size(A, 2) == size(B, 2)), otherwise RunMat raises the MATLAB error "Matrix dimensions must agree."
• Underdetermined and overdetermined systems return the minimum-norm least-squares solution.

Does RunMat run mrdivide on the GPU?

When a gpuArray provider is active, RunMat first offers the solve to its mrdivide hook. The WGPU provider currently downloads the operands to the host, executes the same SVD-based solver used by the CPU implementation, then uploads the result back to the device so residency remains transparent. If no provider is available—or the provider declines the request—RunMat gathers any gpuArray inputs to the host, computes the solution, and returns a host tensor.

GPU memory and residency

No manual care is required. If both operands already reside on the GPU and the provider supports mrdivide, the solve stays on the device. When the provider falls back to the host (the current WGPU implementation), the runtime seamlessly gathers data, executes the solve, and re-uploads the result to keep downstream GPU pipelines working as expected.

Examples

Solving a square linear system

A = [1 2; 3 4];
B = [5 6; 7 8];
X = A / B;

% Verify the solution
residual = X * B

Expected output:

X =
     3    -2
     2    -1

residual =
     1     2
     3     4

Computing a least-squares right division

A = [1 2 3];
B = [1 0 1; 0 1 1];
X = A / B

Expected output:

X = [1 2]

Dividing by a scalar

A = [2 4 6];
scaled = A / 2

Expected output:

scaled = [1 2 3]

Right division with complex inputs

A = [1+2i 3-4i];
B = [2-i 1+i];
X = A / B

Expected output:

X = -0.1429 - 0.2857i

Using mrdivide with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how mrdivide changes the result.

FAQ

Related Linalg functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how mrdivide is executed, line by line, in Rust.

• View the source for mrdivide in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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