Repository: pytorch
Issue: linalg.ldl_factor raises an error with zero tensor
Labels: triaged,module: mkl,module: linear algebra

Repro steps:
```
import torch
torch.linalg.ldl_factor(torch.tensor([[0.0]]))
```
errors out with:
```
RuntimeError: false INTERNAL ASSERT FAILED at "../aten/src/ATen/native/BatchLinearAlgebra.cpp":1568, please report a bug to PyTorch. torch.linalg.ldl_factor: Unknown error code: 1.
```
Note that:
* `torch.linalg.ldl_factor_ex(torch.tensor([[0.0]]))` succeeds,
* `torch.linalg.ldl_factor(torch.tensor([[-1.0]]))` succeeds
* the issue also flares up if one eigen value is exactly 0.

### Versions

```
PyTorch version: 2.1.0+cu121
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: 14.0.0-1ubuntu1.1
CMake version: version 3.27.9
Libc version: glibc-2.35

Python version: 3.10.12 (main, Nov 20 2023, 15:14:05) [GCC 11.4.0] (64-bit runtime)
Python platform: Linux-6.1.58+-x86_64-with-glibc2.35
Is CUDA available: False
CUDA runtime version: 12.2.140
CUDA_MODULE_LOADING set to: N/A
GPU models and configuration: Could not collect
Nvidia driver version: Could not collect
cuDNN version: Probably one of the following:
/usr/lib/x86_64-linux-gnu/libcudnn.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_adv_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_adv_train.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_cnn_train.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_ops_infer.so.8.9.6
/usr/lib/x86_64-linux-gnu/libcudnn_ops_train.so.8.9.6
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, 48 bits virtual
Byte Order:                         Little Endian
CPU(s):                             2
On-line CPU(s) list:                0,1
Vendor ID:                          GenuineIntel
Model name:                         Intel(R) Xeon(R) CPU @ 2.20GHz
CPU family:                         6
Model:                              79
Thread(s) per core:                 2
Core(s) per socket:                 1
Socket(s):                          1
Stepping:                           0
BogoMIPS:                           4400.31
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 rep_good nopl xtopology nonstop_tsc cpuid tsc_known_freq pni pclmulqdq ssse3 fma cx16 pcid sse4_1 sse4_2 x2apic movbe popcnt aes xsave avx f16c rdrand hypervisor lahf_lm abm 3dnowprefetch invpcid_single ssbd ibrs ibpb stibp fsgsbase tsc_adjust bmi1 hle avx2 smep bmi2 erms invpcid rtm rdseed adx smap xsaveopt arat md_clear arch_capabilities
Hypervisor vendor:                  KVM
Virtualization type:                full
L1d cache:                          32 KiB (1 instance)
L1i cache:                          32 KiB (1 instance)
L2 cache:                           256 KiB (1 instance)
L3 cache:                           55 MiB (1 instance)
NUMA node(s):                       1
NUMA node0 CPU(s):                  0,1
Vulnerability Gather data sampling: Not affected
Vulnerability Itlb multihit:        Not affected
Vulnerability L1tf:                 Mitigation; PTE Inversion
Vulnerability Mds:                  Vulnerable; SMT Host state unknown
Vulnerability Meltdown:             Vulnerable
Vulnerability Mmio stale data:      Vulnerable
Vulnerability Retbleed:             Vulnerable
Vulnerability Spec rstack overflow: Not affected
Vulnerability Spec store bypass:    Vulnerable
Vulnerability Spectre v1:           Vulnerable: __user pointer sanitization and usercopy barriers only; no swapgs barriers
Vulnerability Spectre v2:           Vulnerable, IBPB: disabled, STIBP: disabled, PBRSB-eIBRS: Not affected
Vulnerability Srbds:                Not affected
Vulnerability Tsx async abort:      Vulnerable

Versions of relevant libraries:
[pip3] numpy==1.25.2
[pip3] torch==2.1.0+cu121
[pip3] torchaudio==2.1.0+cu121
[pip3] torchdata==0.7.0
[pip3] torchsummary==1.5.1
[pip3] torchtext==0.16.0
[pip3] torchvision==0.16.0+cu121
[pip3] triton==2.1.0
[conda] Could not collect
```

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