Repository: pytorch
Issue: gesvda driver of svd returns nan for zero matrix
Labels: triaged,module: linear algebra

### 🐛 Describe the bug

```python
import torch

torch.linalg.svd(torch.zeros(3,3).cuda(), full_matrices=False, driver='gesvda')
```

![image](https://github.com/user-attachments/assets/97b7876a-3a95-442b-a523-f568b8d39e50)


### Versions

PyTorch version: 2.3.1
Is debug build: False
CUDA used to build PyTorch: 12.1
ROCM used to build PyTorch: N/A

OS: Ubuntu 22.04.3 LTS (x86_64)
GCC version: (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0
Clang version: Could not collect
CMake version: Could not collect
Libc version: glibc-2.35

Python version: 3.10.14 | packaged by conda-forge | (main, Mar 20 2024, 12:45:18) [GCC 12.3.0] (64-bit runtime)
Python platform: Linux-5.15.0-94-generic-x86_64-with-glibc2.35
Is CUDA available: True
CUDA runtime version: 12.2.140
CUDA_MODULE_LOADING set to: LAZY
GPU models and configuration: 
GPU 0: NVIDIA H100 80GB HBM3
GPU 1: NVIDIA H100 80GB HBM3
GPU 2: NVIDIA H100 80GB HBM3
GPU 3: NVIDIA H100 80GB HBM3
GPU 4: NVIDIA H100 80GB HBM3
GPU 5: NVIDIA H100 80GB HBM3
GPU 6: NVIDIA H100 80GB HBM3
GPU 7: NVIDIA H100 80GB HBM3

Nvidia driver version: 535.154.05
cuDNN version: Could not collect
HIP runtime version: N/A
MIOpen runtime version: N/A
Is XNNPACK available: True

CPU:
Architecture:                       x86_64
CPU op-mode(s):                     32-bit, 64-bit
Address sizes:                      46 bits physical, 57 bits virtual
Byte Order:                         Little Endian
CPU(s):                             176
On-line CPU(s) list:                0-175
Vendor ID:                          GenuineIntel
Model name:                         Intel(R) Xeon(R) Platinum 8468V
CPU family:                         6
Model:                              143
Thread(s) per core:                 2
Core(s) per socket:                 44
Socket(s):                          2
Stepping:                           8
BogoMIPS:                           4800.00
Flags:                              fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush mmx fxsr sse sse2 ss ht syscall nx pdpe1gb rdtscp lm constant_tsc arch_perfmon rep_good nopl xtopology nonstop_tsc cpuid tsc_known_freq pni pclmulqdq vmx ssse3 fma cx16 pdcm pcid sse4_1 sse4_2 x2apic movbe popcnt tsc_deadline_timer aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch cpuid_fault invpcid_single ssbd ibrs ibpb stibp ibrs_enhanced tpr_shadow vnmi flexpriority ept vpid ept_ad fsgsbase tsc_adjust bmi1 avx2 smep bmi2 erms invpcid avx512f avx512dq rdseed adx smap avx512ifma clflushopt clwb avx512cd sha_ni avx512bw avx512vl xsaveopt xsavec xgetbv1 xsaves avx_vnni avx512_bf16 wbnoinvd arat avx512vbmi umip pku ospke waitpkg avx512_vbmi2 gfni vaes vpclmulqdq avx512_vnni avx512_bitalg avx512_vpopcntdq la57 rdpid bus_lock_detect cldemote movdiri movdir64b fsrm md_clear serialize tsxldtrk avx512_fp16 arch_capabilities
Virtualization:                     VT-x
Hypervisor vendor:                  KVM
Virtualization type:                full
L1d cache:                          4.1 MiB (88 instances)
L1i cache:                          2.8 MiB (88 instances)
L2 cache:                           176 MiB (88 instances)
L3 cache:                           195 MiB (2 instances)
NUMA node(s):                       2
NUMA node0 CPU(s):                  0-87
NUMA node1 CPU(s):                  88-175
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit:        Not affected
Vulnerability L1tf:                 Not affected
Vulnerability Mds:                  Not affected
Vulnerability Meltdown:             Not affected
Vulnerability Mmio stale data:      Not affected
Vulnerability Retbleed:             Not affected
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass:    Mitigation; Speculative Store Bypass disabled via prctl and seccomp
Vulnerability Spectre v1:           Mitigation; usercopy/swapgs barriers and __user pointer sanitization
Vulnerability Spectre v2:           Mitigation; Enhanced IBRS, IBPB conditional, RSB filling, PBRSB-eIBRS SW sequence
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Mitigation; TSX disabled

Versions of relevant libraries:
[pip3] numpy==1.26.4
[pip3] torch==2.3.1
[pip3] torchaudio==2.3.1
[pip3] torchvision==0.18.1
[pip3] triton==2.3.1
[conda] blas                      2.116                       mkl    conda-forge
[conda] blas-devel                3.9.0            16_linux64_mkl    conda-forge
[conda] libblas                   3.9.0            16_linux64_mkl    conda-forge
[conda] libcblas                  3.9.0            16_linux64_mkl    conda-forge
[conda] liblapack                 3.9.0            16_linux64_mkl    conda-forge
[conda] liblapacke                3.9.0            16_linux64_mkl    conda-forge
[conda] libopenvino-pytorch-frontend 2024.2.0             he02047a_1    conda-forge
[conda] mkl                       2022.1.0           h84fe81f_915    conda-forge
[conda] mkl-devel                 2022.1.0           ha770c72_916    conda-forge
[conda] mkl-include               2022.1.0           h84fe81f_915    conda-forge
[conda] numpy                     1.26.4          py310hb13e2d6_0    conda-forge
[conda] pytorch                   2.3.1           py3.10_cuda12.1_cudnn8.9.2_0    pytorch
[conda] pytorch-cuda              12.1                 ha16c6d3_5    pytorch
[conda] pytorch-mutex             1.0                        cuda    pytorch
[conda] torchaudio                2.3.1               py310_cu121    pytorch
[conda] torchtriton               2.3.1                     py310    pytorch
[conda] torchvision               0.18.1              py310_cu121    pytorch

cc @jianyuh @nikitaved @pearu @mruberry @walterddr @xwang233 @Lezcano