mldivide — Solve linear systems with left-division in MATLAB and RunMat.

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

Syntax

X = mldivide(A, B)

Inputs

Returns

Errors

How mldivide works

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

Does RunMat run mldivide on the GPU?

When a gpuArray provider is active, RunMat first offers the solve to its mldivide hook. The current WGPU provider downloads the operands to the host, executes the shared SVD-based solver, then uploads the result back to the device so downstream GPU pipelines keep their residency. If no provider is available—or a provider declines the request—RunMat gathers gpuArray inputs to the host, performs the solve there, and returns a host tensor.

GPU memory and residency

No manual residency management is required. If both operands already live on the GPU and the active provider implements mldivide, the solve stays on the device. When the provider falls back to the host (as the current WGPU backend does), RunMat gathers data, executes the same SVD solver used by the CPU implementation, and re-uploads the result so subsequent GPU work continues seamlessly.

Examples

Solving a square linear system with backslash

A = [1 2; 3 4];
b = [5; 6];
x = A \ b

Expected output:

x =
    -4.0000
     4.5000

Computing a least-squares solution with backslash

A = [1 2; 3 4; 5 6];
b = [7; 8; 9];
x = A \ b

Expected output:

x =
    -6.0000
     6.5000

Scaling by a scalar using backslash

s = 2;
B = [2 4 6];
scaled = s \ B

Expected output:

scaled = [1 2 3]

Solving multiple right-hand sides at once

A = [4 1; 2 3];
B = [1 0; 0 1];
X = A \ B

Expected output:

X =
     0.3   -0.1
    -0.2    0.4

Left division with complex matrices

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

Expected output:

X =
   -0.0732 - 0.3415i
    0.8049 + 0.7561i

Using mldivide with coding agents

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

FAQ

Related Linalg functions

Open-source implementation

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

• View the source for mldivide 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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